Research ArticleDynamics and Motivations of Media MarketingThe Role of Globalization and Empowerment

Cinzia Colapinto1 and Eleonora Benecchi2

1 Department of Management Carsquo Foscari University of Venice San Giobbe Cannaregio 873-30121 Venice Italy2 Institute of Media and Journalism Universita della Svizzera Italiana Via Buffi 13 6900 Lugano Switzerland

Correspondence should be addressed to Cinzia Colapinto cinziacolapintouniveit

Received 27 February 2014 Accepted 9 May 2014 Published 3 June 2014

Academic Editor Simone Marsiglio

Copyright copy 2014 C Colapinto and E BenecchiThis is an open access article distributed under theCreative CommonsAttributionLicense which permits unrestricted use distribution and reproduction in anymedium provided the originalwork is properly cited

Audience fragmentation convergence and technology development have changed consumption patterns and brand communica-tion Media companies should consider TV series and movies as brands to be exploiting at nationalinternational level Using adynamic diffusionmodel we analyze the evolution of popularity in a specific country under different hypothesesThen we proposean optimal decision model which describes the decision makerrsquos point of view in a two-sided market

1 Introduction

Many changes (such as media convergence transition todigital format and audience fragmentation) are affectingmedia companiesrsquo business model and have given to mediacontent a primary role Indeed media environment haschanged and in order to better satisfy audiencersquos new tastesand consumption paths most broadcasters have been trans-forming into multichannel and multiservices companieswhose supply is characterized by interactivity [1] Companiesactors or sportsmen rely more and more on the power ofnew media and of a viral spread which is heightened byonline communities and the cross-pollination of content onother social media sites [2ndash4] The real value of social mediaconsists in rebuilding the buzz and reinforcing the attitudethat distinguishes the brand from its rivals Media companiesneed to include consumers in their value chain (a real valueconstellation) recalling Tofflerrsquos [5] concept of prosumer thisterm identified consumer involvement in product designnowadays consumers are involved in value creation Contentis now being produced and consumed in innovative waysconsequently internet and new media have become botha viewing site and a site of fan engagement Technologicaladvances lead towards new media content models mainly

based on participatory media [6] Such a new strategy deeplyrelies on consumer behavioursThus focusing on the conceptof brand we believe TV series are an interesting case study

Television programs are a public good and they are soldthrough many different channels over different points intime to maximize profits (windowing) As people are doingtheir best to avoid commercials companies need to aggregateand to encourage customers to come back for more as aresult Internet and new and social media are becoming veryimportant marketing tools The synergistic marketing com-munication [7] implies the use of different channels (oftenthrough synergistic ownership strategies) and approaches topersuasion companies use multiple promotional outlets toreach desirable audiences In particular mediamarketing hasmoved toward the Internet discovering the importance ofviral marketing word of mouth and online communities inall the phases of the life cycle of a product

In a complex evolving system TV programsrsquo and mar-keting investment choices by media managers are gettingmore difficult and complex they need to pursue data-drivendecisions Most analysis tolls consider TV programs ratingsand we propose a decisional dynamic model which utilizesa dynamic model explaining the path of program popularityover time

Hindawi Publishing CorporationAbstract and Applied AnalysisVolume 2014 Article ID 393168 9 pageshttpdxdoiorg1011552014393168

2 Abstract and Applied Analysis

The paper is organized as follows Section 2 introducesthe concept of connected marketing and recalls the fun-damental literature Section 3 is dedicated to the diffusionmodel based on the literature of biological field and therelated examples in this way we intend to shed a light onthe responses of TV series fans and their behaviourWe pointout media managersrsquo choices as well as viewersrsquo actions InSection 4 using real data we test our model and provide thelong run behaviour of an imported TV series Section 5 intro-duces amodel to sustain the decisionmaker (DM) in the con-text of management operational policy Section 6 concludes

2 Connected MarketingThe Consumer-Led Future

It is increasingly clear that Marketing Departments for TVShows behave according to the rule that the more endorse-ments that trickle through blogs forums Facebook andTwitter the better it is Whether online activity especiallysocial media activity could make or break a TV show is stillunclear however it is a fact that networks are increasinglytrying to monitor Internet discussions to gain insight intowhether a show will move from hype to hit Recent dealsbetween the major American networks and research organi-zations such as Networked Insight are proofs of that

Marketing is crucial for media companies to survive andprosper in the current media ecosystem characterized onone hand by an increasing competition for scarce audienceand convergence and on the other by the empowerment ofconsumers Media companies are special because they canbe utilized as communication tools for self-branding [8] Inparticular considering TV series it is evident that fans arebeing exposed to a greater number of products than everbefore That is why developing direct relationship with fansis vital for media companies in the wake of the growingexposure fans have to new products all competing for theirtime and attention In this scenario the role of peers and ofdirect marketing tools (websites social media ) is gettingimportant and Internet shakes up the long-standing balancesof power between fans and the media content makers

The connected marketing approachmdashword of mouthbuzz and viral marketing that is all different techniquesoriginating from the sociological theory of the two-step flow[9]mdashdominates the information society The main charac-teristic is the active role of actual and potential customersand the viral diffusion of messages mimicking the idea ofprosumer

Fandom studies confirm that fans are becoming a relevantif not central part of the new television ecosystem on oneside the crucial role of fans in the new media ecosystem isenlightened by studies portraying fans as a selected but strate-gic audience for TV producers (fan as super-consumers) andtherefore focusing on the incorporation of fan practices bythe TV industry [10ndash12] on the other side the power offandom is recognized in its growing influence on creativeand productive choices made by TV showsrsquo creators (fansas creative subjects) and therefore the focus is on changingrelationship between producers and consumers [13ndash15]

Considering fans either super-consumers or creativesubjects recent field studies demonstrated that media con-glomerates have becomemore aware of how fan creations canadd to and affectmedia product developmentmarketing anddistribution Therefore they seek to harness fan activities forlow-cost and effective advertisements [14 16] Neverthelessit is also true that the monetization of fan creations is not aneasy aim to accomplish fans show an anticommercial natureand embrace a gift economy model [17] often refusing to beincorporated in the commercial production process [11]

All techniques are exploited in the digital ecosystemFeedback opportunities provided by Web 20 technologiesrepresent both new chances for audience engagement andnew challenges for the television industry [13 18] Insteadof replacing television the Web seems to have embracedit and with regard to TV series the Internet seems tohave turned television into a shared event for the mostpassionate viewers who have become plugged-in mainlysharing the show with the other viewers [19ndash21] Indeedthrough online communities passionate viewers find andshare a privileged knowledge which is derived both from theviewing experience and the extratextual elements of the TVprogram [21] Fans try to influence TV series productionpromotion and distribution in two main ways (a) activelypetitioning a TV network to keep a show on air and (b)participating online in official and unofficial promotionalactivities in order to keep communication about the showalive

As we said it is interesting to go beyond the oppositionbetween producer and consumer focusing on the role of fancommunities in promoting TV series within the frameworkof the gift economy [14 22ndash24] The media product is agift which the receiver can reciprocate through attentionfeedback fandom or even purchasing advertised productsIn particular digital environments embrace the reply insteadof reciprocation it means giving a feedback to the authoror passing along to others Media fandom is a battlegroundwhere the territory between online gift economies andcommodity culture will be negotiated

In this paper we focus on American TV series which arebuilt in order to be ldquodistributedrdquo to an international audience[15] and use transmedia storytelling [25] as a promotionalstrategy to engage a wide and dispersed audience Indeedmany TV series have been distributed with success inEuropean countries giving birth to strong fan communities[26 27]

There exists a correlation between TV programsrsquo ratingsand choices (even the choice of doing nothing) by the DMratings act as a proxy of the product quality However theDMcannot completely control the program popularity becauseof the consumer empowerment Media marketing managersusually pursue all possible actions to back a TV program andlimit the risk of failure However this is a costly behaviourand understanding the impacts of specific actions is crucialto reduce investments and increase returns To concludeit is evident that popularity is affected and sustained notonly by media managersrsquo decisions as viewers are empow-ered Indeed in Section 3 the model will consider bothagents

Abstract and Applied Analysis 3

3 Popularity of TV Series A Dynamic Model

Connected marketing is used to underpin the popularity of abrand or a productThe success is affected by the capability ofgenerating engagement with customers and the engagementis relevant if we consider media content

From now on let 119875(119905) be a time dependent variablewhich describes the degree of popularity of a given productat the time 119905 We now formulate a model (similar modelshave been used in different contexts such as economicgrowth population dynamics and technology diffusion)which describes the behaviour of119875 over time and allows us todraw long run analysis We consider a local analysis in otherwords the diffusion path occurring in a specific country Weassume that popularity is driven by the following differentialequation

119889119875 (119905)

119889119905

= (120578 minus 120575) 119875 (119905) + 120591(1)

where

(i) 120575 is the natural depreciation rate (0 lt 120575 lt 1) ofpopularity Every product or service has a life cycleand when the market is mature it enters the declinestage and may die This term is also linked to thecultural discount [28] that is a particular program isrooted in one culture and thus is attractive in thatenvironment whilst it shall have diminished appealelsewhere The higher the cultural discount is thehigher the depreciation rate is

(ii) 120578 describes the actionsmade by the decisionmaker tosupport the campaign and by the other customers tospread information concerning the product

(iii) 120591 is an exogenous factor which takes into accountthe influence of the popularity of the product abroadA negative value means that the product failed in aforeign market and had a bad reputation which canaffect the campaign in the country under analysis Apositive value represents the success of the productor service abroad which can be translated in positivenetwork externalities in the country under analysisEven if it is a local model we have to consider theeffects derived from information flows and the trackrecords of the product elsewhere

It is possible to show that model (1) admits a solution of theform (120578 = 120575)

119875 (119905) = (119875 (0) +

120591

120578 minus 120575

) 119890

(minus120575+120578)119905minus

120591

120578 minus 120575

(2)

This kind of dynamic model formulated in terms of differen-tial equation has been widely used in the economic and socialscience literature to describe the evolution of variables such asinnovation population and human capital (see for instance[29ndash32]) If 120578 = 120575 the above model (1) becomes trivial and itadmits either a constant solution or a linear behavior (120591 = 0or 120591 = 0 resp)

4 Model Discussion

In the following discussion we present for each possible solu-tion a set of cases that could represent a concrete occurrenceof the solution itself The examples we are providing areonly explanatory and limited to the field of American TVseries imported in Italy We decided to focus on AmericanTV series for different reasons First foreign TV series andespecially American ones have historically dominated theItalian television market This gave us a sample which wasinternally coherent but provided also awide set of cases to testour model with Since we are taking into consideration notonly marketing actions undertaken by the local networks inorder to support specific TV series but also cultural practicesand fan activities that helped even unsupported TV series togain strength in the local market the fact that a remarkablenumber of American TV series had successfully conqueredthe Italian public despite the inherent cultural differencesbetween those shows and the local audience strategic [33]was also an influential factor in choosing our sample

(A) 120591 = 0 and 120578 = 0 This is the case in which there is noinfluence from abroad and no actions are undertakenThe solution to (1) is given by 119875(119905) = 119875(0)119890minus120575119905 As aresult 119875 goes to zero in the long run (Figure 1) thepopularity tends naturally to fade away If the decisionmaker does not intervene the attention of consumerswill focus on something else

This was the typical case of American TV series boughtthrough an output deal where the Italian broadcasters agreedto buy everything a specificmajor produces for an establishedperiod of timeThis kind of blind agreement obviously leadsto the purchase of TV series that are not strategic or evenadapted to the broadcasting network entitled to air themIn many cases Italian TV channels used those ldquoresidualrdquoproducts to fill up the night schedule or the many ldquovoidrdquospaces of a full day schedule This meant that the popularityand ratings of the TV series abroad were not influential inchoosing the time slot in which the products were aired northe broadcasting network felt the need to promote or push theproduct inside the local market

One classic example of the case in which there is noinfluence from abroad and no actions is the prime timedrama Angel (1999) a spin-off of the more popular Buffy theVampire Slayers produced by Warner Bros and purchasedin Italy by Mediaset The TV series was broadcasted inItaly by the private channel Italia 1 which had been airingBuffy as well in the overnight programming and with anerratic schedule It must be said that the purchase of Angelwas a direct consequence of the previous purchase of Buffyand not a strategic choice and this explains the lack ofldquorespectrdquo for the product both in its airing strategy and inits adaptation In this case the popularity of the series abroadhad no influence in the marketing and distribution in Italyand the degree of popularity of the TV series in the localmarket faded away quickly despite the huge popularity ofits mother series Buffy in the same market The fact thatItalia 1 never invested in the promotion of Angel and didnot intend to profit from the popularity of the series abroad

4 Abstract and Applied Analysis

1

08

06

04

02

0

P

0 20 40 60 80 100

t

Figure 1 Popularity fades away

ignoring it instead was crucial to the lack of success of theseries the airing of which was stopped after the third seasondespite that there were other two seasons to go before theproduction was stopped This is even clearer now since thesameTV series has been aired by the digital channel Rai4withdiscrete success Indeed the airing of American TV series ina new uncensored version and in day-time was crucial tothe success of the digital channel which reached a share of130 on the national level in 2009 ranking third among themost viewed national channels digitally broadcasted (Auditeldata season 2009 34) The promotion of Angel proposed byRai4 was aimed at profiting from its international ldquocult statusrdquoand underling strategic importance of the TV series for thedigital channel itself Headlines such as ldquofor the first time inprime timerdquo and ldquothe cult series in a new version only onRAI4rdquowere used among others to sustain those promotionalideas The launch was backed by serial fans on their blogs(see fi httpantoniogennawordpresscom20090528tv-)dig-angel-arriva-su-rai-4) Moreover Rai4 bets on interac-tivity and digital communication and has also Facebook andTwitter accounts in order to discuss with viewers

Another example is the American TV drama Supernat-ural Since its first airing on 13th September 2005 the CWprime time TV show became a fan favourite as acknowl-edged by TV critics and fandom experts [34ndash36] Despite aldquorabid fan followingrdquo and the identification of ldquocult showrdquoSupernatural was never a hit show What is relevant to thisstudy is that theCWhas never highly promoted Supernaturalsince the WB and UPN merged into the new network backin 2006 in comparison with its other prime time series Thelow promotion was combined during the 7 years of airingwith a schedule hopping from Tuesday toThursday to FridayThis fact was admitted in official statements by the CW com-munication executives who justified the lack of promotionwith the acknowledgment that Supernatural was considereda ldquoproven veteranrdquo that had already established itself andshould allow newcomers to ldquogain additional exposurerdquo [37]

Nevertheless the lack of promotion by the CW could beaccording to our model one of the reasons for the deceasingratings for the show Interestingly the same treatment in termof lack of promotion and erratic scheduling has been givento Supernatural in its Italian adaptation (see Section 41)

(B) 120591 = 0 and 120578 = 0 We assume that the actions dependon the degree of popularity and that the trend is linearThis approach is quite similar to the viral equationused by many researchers In this case the solution is119875(119905) = 119875(0)119890

(120578minus120575)119905 and two scenarios can happen

(a) If 120578 gt 120575 then 119875 will increase providing asuccessful campaign

The first five years ofThe Bold and the Beautiful (1987) in USwere not a good start for the CBS soap it was in fact thenetworkrsquos lowest-rated soap In this case though the aim ofthe producers was to create an international success and nota national one In fact since its first airing the soap has becomethe most-watched soap in the world with an audience of anestimated 262 million viewers [37] In Italy the investmentmade on the soap simply known as Beautiful was huge interms of promotion and distribution since the beginning ofits airing in 1990The soapwas scheduled in a crucial daytimetimeslot (1345) on Raidue and later on even in prime timewith a rhythm of 3 episodes per night In 1994 the soapwas bought by Mediaset but the daytime slot remained thesame even when the series started its airing on Canale5This was a crucial point in the promotional campaign whichstated that ldquothe lunch time is always beautifulrdquo stating thehappy marriage between Beautiful and the 1340 time slotThe faithfulness of the Italian audience toward the soap wasbuilt over time and based on the strategic scheduling thecollaboration between the American producers andMediasetgroup which lead to the setting of many storylines in Italy(f i Venezia 1997 Como 2000 and Portofino 2007) theinvestments in the promotional area that lead to localizedpromos with the leading actors and frequent visits from thecast in Italian talk shows and entertainment programs (lastof which was the participation of Ronn Moss the leadingmale actor in the Dancing with the stars Italian edition)and the investments in the distribution area with specialedition DVD sold in kiosks specialized volumes publishedby Mediaset Group and a reair of the daytime episodes inprime time on Mediaset digital platforms (La5 channel) Theratings for the American soap reflected its popularity in Italywith episodes reaching the record of 7 million viewers anda 37 share and more than 400 episodes with 6 millionof viewers each (Auditel data 34) Interesting enough theinternational success in this case reverberated on the originalcountry of production in two ways for once the soap waskept under production because of the selling power registeredabroad secondly the popularity of the show abroad seemedto affect the national audiences and by the mid-to-late 1990sthe numbers of the soap begun to climb and in the 2000sconstantly held the second position in the Nielsen weeklyratings for daytime dramas

Abstract and Applied Analysis 5

(b) If 120578 lt 120575 the product is not able to gain attentionand in the long run people will forget it

Women Murders Club a legal drama which ran on ABCfrom October 12 2007 to May 13 2008 was affected by the20072008 Writers Guild of America and by the subsequenterratic programming after the first 10 episodes were airedpeople had to wait 4 months to see the last 3 episodes theshow was also put in the Friday night prime time slot whichis considered a ldquodeath slotrdquo due to the concept that manyshows scheduled on or moved to Friday nights would not lastlong before cancellation due to low ratings From a receptionpoint of view not only the ratings were low (first seasonranked 57th with a medium of 8964m viewers) but alsothe critical response was tepid with Goodman [38] the SanFrancisco Chronicle TV critic publishing a highly criticalreview assigning the paperrsquos lowest possible rating and theNew York Times TV critic Stanley describing the show as ldquoallright but not good enoughrdquo [39] In fact Women MurdersClubwas cancelled onMay 12 2008 Mediaset had purchasedthe drama series before the strike judging just from the pilotand could not of course forecast the damages the strike wouldhave had on the development and even the ratings of manyAmerican TV showsWomenMurders Club suddenly becamean unwanted product because of the fast cancellation and thelack of popularity in the original country Mediaset ran theTV series first on the digital channel Joy part of its PremiumGallery and later because of the general lack of attentiondecides to use it to fill up the prime time slot of Canale5during the summer of 2010 The choice of programming anew drama series outside the guarantee period (11 Januaryndash30 June) is unusual but wise in this case the tepid receptionof the TV series first run both in US and in Italy the lack ofa previous successful campaign and of previous good resultsto build from and the small number of episodes availableconvinced the network that the series could not be consideredstrategic despite the fact that it was consistent to the channelidentity and target Women Murders Club is then offered tothe summer audience as a gift with a promotion built aroundits unusual scheduling (ldquoCanale5 offers you something neweven if it is Summerrdquo) and its resemblance to more populardramas (ldquoA mix between CSI Sex and The City and GreyrsquosAnatomyrdquo) The series is then used up as fast as possible inthe first week 4 episodes are aired in two nights (Tuesday andThursday) and from the second week the series is aired witha rhythm of 2 episodes per night on Thursday After a goodstart (1472 share and winner of the prime time) the ratingsdrop down week after week and the TV series is constantlysurpassed by old episodes of the scientific program Quarkaired by RAI in the same timeslot

(C) 120591 = 0 Under these hypotheses the solution is 119875(119905) =(119875(0)+120591(120578minus120575))119890

(120578minus120575)119905minus120591(120578minus120575) Different scenarios

can occur

(a) If 120578 gt 120575 then 119875 will increase providing asuccessful campaign whatever is the influencefrom abroad great investments in creating a

fandom would overturn the performance anddecrease the effects of bad reputation

The TV series Tequila and Bonetti (1992) inspired by themore popular movie Turner and Hooch (1989) starring TomHanks was aired by CBS from January 17th to April 18th1992 The detective comedy series was not a very successfulone and was cancelled after only 12 episodes Despite thatit proved to be a perfect match for the Italian channelItalia1 which aired the series repeatedly during the 1990sThe popularity of the TV series remained stable even aftermany years had passed since its last airing so much thatRete4 (Mediaset Group) started airing the TV series againin November 2009 What is even more interesting is thatafter 8 years from its cancellation in US a new season ofthe TV series was produced in Italy under the new title ofTequilaampBonetti (MastrofilmMediaTradeColumbia TriStarInternational Television 2000) Promotion and localizationof the series (Nick Bonetti was ldquotransferredrdquo in Rome andpartnered with an Italian celebrity in her first acting role)were independent from the American production and dis-tribution so much that the original producer Don Bellisarioonly discovered the existence of this second series years afterits first airing in Italy with obvious consequent legal issuesThe ldquolocalizedrdquo second season of the original American serieswas gifted with similar success and the 22 episodes airedrepeatedly on Italia1 and later on the satellite channels SkyShow (2008) and Sky Uno (2009) In this case the investmentin the promotion and adaptation of the TV series was hugedespite the lack of success of the product in the originalcountry of production

(b) If 120578 lt 120575 the popularity will tend to minus120591(120578minus120575) Inthis case the reputation and popularity abroadreally drive the internal performance

(b1) If 120591 is positive then the long run results ofthe campaign will end up in a success casewhose intensity is proportional to 120591

In this case the popularity of the TV series in the local marketis connected with the popularity of the TV series abroad CSIMiami (2002) the first spin-off of the forensic drama CSIarrived in Italy at the end of 2003 after the huge successregistered by the original CSI on the channel Italia1 and theevenmore huge success of the show in the worldwidemarketIt was not necessary to build up a big promotional campaignfor the TV series because the international success of the CSIfranchise was speaking for itself Later on CSI Miami waseven named the most popular program in the world becauseit featured in more countriesrsquo top 10 rankings for 2005 thanany other [40] and this data was used in the Italian promosfor the show Building from the international success of thefranchise and of the TV series itself CSI Miami soon becameone of themost viewed programs ofWednesday night and themost viewed series between the CSI franchises in Italy Theconfidence in the Italian success of CSI Miami is so strongthat in 2006 the series was even used to counterbalance theflop of the third season of The OC replacing the teen dramaon Sunday night and airing twice a week for months

6 Abstract and Applied Analysis

(b2) If 120591 is negative the fail in the foreign coun-tries will imply a decreasing popularity andeven worse the creation of people spreadingnegative comments on the product

This was the case of Defying Gravity a multinationallyproduced space travel drama which first aired on ABCin August 2009 The low ratings convinced the Americannetwork to suspend the series even if only 8 episodes outof the 13 produced had been aired When the debacle of theseries abroad was clear the Italian satellite channel Sky hadalready purchased the full first season and decided to air theproduct anyway on Fox Life starting 12 June 2010 in the lateprime time-slot (2155) The promotion and distribution ofthe show could not in this case profit from the internationalsuccess and had instead to fight against the bad popularity ofthe TV series which was even more evident because of thehigh profile promotion made in the original countryDefyingGravitywas in fact supposed to have 6 seasons 6 years was infact the length of the interplanetary voyage which plannedto visit most of the planets of the Solar System and wasmarketed as ldquoa Greyrsquos anatomy set in spacerdquo establishing adirect link with the most successful medical drama of ABCand playing with the fact that the two series had the sameproducing teamThis kind of promotionmade the seriesrsquo flopevenmore problematic for the international broadcasters Skyreused the ABC reference to Greyrsquos Anatomy a huge successin the Italianmarket too but tried to obscure any reference tosci-fi selling the show as a soap and adding to the main titlethe subtitle ldquothe galaxy of heartsrdquo The choice of schedulingDefying Gravity on Fox Lifemdashdedicated to family dramaand medicalsmdashand the late night summer slot-time thoughwere clear indications that the product was not consideredstrategic anymore because of the bad reputation it had gainedabroad

If 120578 = 0 then the popularity will tend to 120591120575 Thisis the case in Italy of the Law and Order franchise (1990)the success (120591 gt 0) of which is obviously disconnectedfrom the amount of local investments the dedication of thebroadcasting networks in the promotion and distributionarea for the single series in fact has always tended to zero inItaly This is shown by the small number of promos realizedfor each series all through their airing by the scheduling ofall the series in the late night or even in the night-time slotsand by the fact that they have been running both on RAIand Mediaset channels with no intention of connecting thesingle series to the specific channels Law and Order SVU forinstance has been used by Rete4 to fill up void spaces in thelate night schedule (between October and November 200710 out of the 22 episodes of the first season were aired inno particular order) before becoming the regular fill for thelate night time slot of the channel Law and Order timesloton Raidue often changed from daytime to late night andback again depending on the nature of the single episodewhile the 17th season (last one of the original series) has beenmoved to the prime time of Raitre Despite all the changes andlack of promotion the constant popularity of the TV seriesabroad and the strong niche following in Italy has made of

02468101214161820

0 20 40 60 80 100

times105

Figure 2 Popularity of Supernatural fades away

the Law and Order franchise a reliable show with specialregards to the ratings which remain constant

41 An Empirical Evidence As mention above in ItalySupernaturalrsquos performance has been affected by the lack of(or scarce) promotion and erratic scheduling (in particularshifting from springtime to summer a season characterizedby lower audience data)

Figure 2 shows the Auditel data [41] of the first four seriesof Supernatural broadcast on Rai2 channel in the period2007ndash2010 in detail the first season was broadcast duringFebruary-July 2007 the second June-September 2008 thethird July-September 2009 and the fourth July-August 2010The x axis shows the sequence of episodes whilst the y axislists the corresponding audience data

Figure 2 suggests that there are fluctuations of the dataaround the black trend line whose intensity is decreasingover time However Supernaturalrsquos long-run behavior can bewell approximated by the function 119875(119905) = 106119890minus0013119905 thatshows an exponential decay of popularity In particular thisempirical evidence shows that 120578 minus 120575 = minus0013 that is 120578 lt 120575implying that either 120578 = 0 (lack of promotion) or nonzero120578 lt 120575 (scarse promotion)

The parametric estimation has been done using thetechnique presented in [42 43] and based on the solution ofan inverse problem for a differential equation

5 An Optimal Decision ModelThe Decision Maker View Point

In a media company the decision maker faces the problemof maximizing profits subject to some constraints Mediacompanies must cover their costs (license fees productioncosts of programs ) and create returns just as any otherbusiness [44]The above formulatedmodel is purely dynamicand that does not provide any optimal decision rule Thepurpose of this section is indeed to formulate a dynamicprogramming model that can fully describe the complexityof a decision making process [45 46] We assume we havea closed market in which there is no influence of thepopularity of the product abroad and then 120591 is assumed to be

Abstract and Applied Analysis 7

zero With respect to the purely dynamic model previouslydescribed in which the term 120578 was supposed to be constantin this context we assume that 120578(119875(119905)) = Ω119875(119905) minus 120587(119905) whereΩ119875(119905) represents the revenues (depending on the level ofpopularity) that a TV company receives from the sale of adspaces to advertisers (Ω can be interpreted as the price of adspace) while 120587(119905) are the profits to be maximized by the DM

The difference Ω119875(119905) minus 120587(119905) is the investment in amarketing campaign The DM tries to maximize hisherintertemporal utility subject to a dynamic constraint thatdescribes the evolution of popularity and it can be formulatedas follows

Max int+infin

0

119880 (120587 (119905)) 119890

minus120588119905119889119905

st 119889119875 (119905)119889119905

= (minus120575 + Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

119875 (0) = 1198750

(3)

where 120588 is the discount rateThe variable 119875(119905) is the state variable while 120587(119905) is the

control For simplicity we assume a logarithmic utility119880 thatis 119880(120587(119905)) = ln(120587(119905)) even if other utility expressions couldbe considered analogously The following result states theexistence of a nontrivial equilibrium for the above dynamicmodel

Proposition 1 Suppose 120588 gt 120575 Then the above model showsthe existence of a nonzero equilibrium (119875lowast 120587lowast) where

119875

lowast=

120588

Ω

120587

lowast= 120588 minus 120575

(4)

Proof It is provided in the Appendix

In other words if the technical condition 120588 gt 120575 issatisfied this dynamic model shows the existence of a non-trivial equilibrium (119875lowast 120587lowast)The equilibrium of popularity119875lowastdepends on the price Ω and the higher will be the cost of amedia product for a customer the lower will be the level of119875lowastHowever as the analytical discussion in the Appendix showsthis equilibrium is unstable this practically means that onlyunder strict conditions the popularity will not vanish in thelong run

6 Conclusions

Internet provides tools that can alter the whole experienceof watching television giving access to the process not justthe results Through online communities in fact passionateviewers find and share a privileged knowledge which isderived both from the viewing experience and the extratex-tual elements of the show [21] According to recent studiesfans aremaking a new kind of television scene that transcendsplace and shakes up long-standing balances of power betweenfans and the television makers In general the most recentliterature published in the field of fan studies suggests that

the line between consumption and production is blurringinto a new paradigm with fans growing up to be creators andcreators trying to connect and engage with fan communitieswhen not labeling themselves as fans [13 21 47]

Themost successful TV series analyzed in this study havein fact been created promoted and distributed not onlytaking into account the existence of an active and internet-based fan audience but also relying on this same audience inorder to make the series an international success Comparedwith the ones that did not profit from the presence of afan audience or did not use connected marketing strategiesthese TV series have indeed succeeded in generating deepperpetual audience engagement

From a previous desk research and exploratory analysis[48] it emerged in fact that (a) there is a willingness toconsume texts offered by producers in different formatsoutside of the narrative space of the show itself and (b) partof the reason for this extratextual success lies in the initialconstruction and marketing of the show itself

Building from these results the model we propose heretries to identify and explain the main factors on whichthe popularity of American TV series in Italy is basedAll the examples confirm in fact the relevance of collateralactions specifically web orientated to underpin the successof televisionrsquos content as well as the influence of foreign popu-larity (globalization) which can be considered the explainingvariable involved in the success of a media product

The paper also introduces a decisional dynamic modelable to sustain the DM in hisher decisions In the Italianscenario commercial television plays a predominant role andcompetes to attract viewersrsquo attention and then sells thatattention to advertisers [49] In other words a broadcastingmedia platform can only succeed if it has viewers otherwiseits revenues from advertising would be zero As it is anadvertisement-supportedmedia from the two-sidedmarketsliterature we know that ad prices reflect both the value ofreaching a given audience and the marginal effect of theadvertisement sale on total audience size Thus popular TVprograms indirectly generate returns for a media companyattracting viewers Our model provides the DM the optimalsolution balancing the investment in sustaining programpopularity and the maximization of profits

For future works we aim at modifying this model byintroducing a stochastic term able to catch the naturalfluctuations arising from audience data

Appendix

In an optimal decision making process the DM tries to solvethe following model

Max int+infin

0

ln (120587 (119905)) 119890minus120588119905119889119905

st 119889119875 (119905)119889119905

= (minus120575 + Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

119875 (0) = 1198750

(5)

8 Abstract and Applied Analysis

The Hamiltonian associated with model (5) is

119867(119875 (119905) 120587 (119905)) = ln (120587 (119905)) 119890minus120588119905 + 120582 (119905)

times (minus120575119875 (119905) + (Ω119875 (119905) minus 120587 (119905)) 119875 (119905))

(6)

Optimality conditions for (6) read as

0 =

120597119867

120597120587

=

119890

minus120588119905

120587 (119905)

minus 120582 (119905) 119875 (119905)

minus

120582 (119905) =

120597119867

120597119875

= 120582 (119905) (minus120575 + 2Ω119875 (119905) minus 120587 (119905))

119875 (119905) =

120597119867

120597120582

= minus120575119875 (119905) + (Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

(7)

The system (7) is equivalent to

120587 (119905) =

119890

minus120588119905

120582 (119905) 119875 (119905)

997904rArr

(119905)

120587 (119905)

= minus120588 minus

120582 (119905)

120582 (119905)

minus

119875 (119905)

119875 (119905)

minus

120582 (119905) = 120582 (119905) (minus120575 + 2Ω119875 (119905) minus 120587 (119905))

997904rArr minus

120582 (119905)

120582 (119905)

= minus120575 + 2Ω119875 (119905) minus 120587 (119905)

119875 (119905) = minus120575119875 (119905) + (Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

997904rArr

119875 (119905)

119875 (119905)

= minus120575 + Ω119875 (119905) minus 120587 (119905)

(8)

which implies

(119905)

120587 (119905)

= minus120588 + Ω119875 (119905)

119875 (119905)

119875 (119905)

= minus120575 + Ω119875 (119905) minus 120587 (119905)

(9)

The only nontrivial equilibrium is

119875

lowast=

120588

Ω

120587

lowast= 120588 minus 120575 gt 0

(10)

The Jacobian of the linearized system at (119875lowast 120587lowast) is equal to

119869 = [

0 Ω (120588 minus 120575)

minus

120588

Ω

120588

] (11)

The determinant of 119869 is equal to

det (119869) = 120588 (120588 minus 120575) gt 0 (12)

while the trace of 119869 is equal to

trace (119869) = 120588 gt 0 (13)

which implies that (119875lowast 120587lowast) is an unstable equilibrium Itis possible to show that this system admits three moreequilibria namely (0 0) (119875lowast 0) and (0 120587lowast) Among them(0 0) and (0 120587lowast) are locally asymptotically stable

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] C Colapinto ldquoMoving to a multichannel and multiplatformcompany in the emerging and digital media ecosystem the caseof mediaset grouprdquo International Journal on Media Manage-ment vol 12 no 2 pp 59ndash75 2010

[2] TWeinbergTheNewCommunity RulesMarketing on the SocialWeb OrsquoReilly Media Inc Sebastopol Calif USA 2009

[3] C Colapinto and E Benecchi ldquoMovie industry goes viral inthe XXIst century if what counts is the buzzrdquo in CrossmediaInnovations I Ibrus and C A Scolari Eds pp 161ndash178 PeterLang Berlin Germany 2012

[4] C Colapinto and E Benecchi ldquoThe presentation of celebritypersonas in everyday twittering managing online reputationsthroughout a communication crisisrdquo Media Culture amp Societyvol 36 pp 219ndash233 2014

[5] A Toffler Future Shock William Morrow and Company NewYork NY USA 1980

[6] L Kung Strategic Management in the Media SAGE LondonUK 2008

[7] M PMcAllister and J Turrow ldquoNewmedia and the commercialsphere two intersecting trends five categories of concernrdquoJournal of Broadcasting amp Electronic Media vol 46 no 4 pp505ndash514 2002

[8] W S McDowell ldquoIssues in Marketing and Brandingrdquo in Hand-book of Media Management and Economics A B Albarran SM Chan-Olmsted and M O Wirth Eds pp 229ndash250 LEANew Jersey NJ USA 2006

[9] E Katz and P F Lazarsfeld Personal Influence The Free PressNew York NY USA 1955

[10] R Ando and A Marinelli ldquoFare ricerca sul fandom on line Ifan italiani e le serie tvrdquo in Sociologia 20 Pratiche Sociali eMetodologie di Ricerca sui Media Partecipativi S Monaci andB Scifo Eds 2010 Scriptaweb httpscriptawebeuCatalogosociologia-2-0

[11] A de Kosnik ldquoShould fan fiction be freerdquo Cinema Journal vol48 no 4 pp 118ndash124 2009

[12] C Sandvoss Fans Polity Press Cambridge UK 2005[13] I Askwith TV 20 turning television into an engagement

medium [MS thesis] 2007 httpcmsmiteduresearchthesesIvanAskwith2007pdf

[14] P BoothDigital Fandom NewMedia Studies Peter Lung 2010[15] J Caldwell ldquoCritical industrial practice branding repurposing

and the migratory patterns of the industrial textsrdquo Television ampNew Media vol 7 pp 99ndash104 2006

[16] H Jenkins S Ford and J Green Spreadable Media NYU NewYork NY USA 2013

[17] E Benecchi and G Richeri ldquoTv to talk about engaging withAmerican tv series through the internetrdquo inThe New TelevisionEcosystem A Abbruzzese and L Fortunato Eds Peter LangBern Switzerland 2013

[18] J T Caldwell Production Culture Duke University PressDurham NC USA 2008

[19] H Jenkins Convergence Culture Where Old and New MediaCollide New York University Press New York NY USA 2006

Abstract and Applied Analysis 9

[20] M Hills Fan Cultures Routledge London UK 2003[21] N Baym Personal Connections in the Digital Age Polity Press

Cambridge UK 2000[22] I Condry ldquoCultures of music piracy an ethnographic com-

parison of the US and Japanrdquo International Journal of CulturalStudies vol 7 pp 343ndash363 2004

[23] AAustinH Jenkins J Green I Askwith and S Ford ldquoTurningpirates into loyalists the moral economy and an alternativeresponse to file sharingrdquo Tech Rep MIT Convergence CultureConsortium Cambridge UK 2006

[24] D Boyd Facebookrsquos Little Gifts Apophenia 2007[25] H Jenkins ldquoLook ListenWalk Technologyrdquo 2004 httpwww

technologyreviewcomInfoTechwtr 13560[26] M Scaglioni TV di culto La Serialita Televisiva Americana e il

Suo Fandom Vita e Pensiero Milano Italy 2006[27] L Porter and D Lavery ldquoCultivating a lost audience the part-

icipatory fan culture of lostrdquo in Unlocking the Meaning ofLost An Unauthorized Guide L Porter and D Lavery EdsSourcebooks Naperville Ill USA 2006

[28] C Hoskins and R Mirus ldquoReasons for the US dominanceof the international trade in television programmesrdquo MediaCulture and Society vol 10 pp 499ndash515 1988

[29] C Colapinto E Sartori andM Tolotti ldquoAwareness persuasionand adoption enriching the bassmodelrdquo Physica A vol 395 pp1ndash10 2014

[30] A Bucci C Colapinto M Forster and D la Torre ldquoStochastictechnology shocks in an extended Uzawa-Lucas model closed-form solution and long-run dynamicsrdquo Journal of EconomicsZeitschrift fur Nationalokonomie vol 103 no 1 pp 83ndash99 2011

[31] V Capasso R Engbers and D la Torre ldquoOn a spatial Solowmodel with technological diffusion and nonconcave productionfunctionrdquo Nonlinear Analysis Real World Applications vol 11no 5 pp 3858ndash3876 2010

[32] D la Torre and S Marsiglio ldquoEndogenous technologicalprogress in a multi-sector growth modelrdquo Economic Modellingvol 27 no 5 pp 1017ndash1028 2010

[33] D Bielby and C HarringtonGlobal TV NYU Press New YorkNY USA 2008

[34] C Tosenberger ldquoSaving people hunting thingsrdquo TransformativeWorks and Culture vol 4 2010

[35] H Jenkins ldquoSupernatural first impressionsrdquo Confessions of anACA-fan 2007 httphenryjenkinsorg200701supernaturalhtml

[36] L Zubernis and K Larsen Eds Fan Phenomena SupernaturalIntellect Books Bristol UK 2014

[37] M Wilson ldquoCW Exec Professes Support for Supernaturalrdquo2008 httpscifiaboutcomb20080122cw-exec-professes-support-for-supernaturalhtm

[38] T Goodman ldquoWomenrsquosMurder Club-bonding over crimerdquo SanFrancisco Chronicle October 2007

[39] A Stanley ldquoHomicide and Heelsrdquo The New York TimesOctober 2007

[40] Informa Telecoms and Media ldquoWorld most popular showsrdquoRadio Times August 2006

[41] ldquoAuditel datardquo httpwwwauditelit[42] H E Kunze D la Torre and E R Vrscay ldquoInverse problems

for random differential equations using the collage method forrandom contraction mappingsrdquo Journal of Computational andApplied Mathematics vol 223 no 2 pp 853ndash861 2009

[43] H Kunze D la Torre and E R Vrscay ldquoA generalized collagemethod based upon the Lax-Milgram functional for solvingboundary value inverse problemsrdquo Nonlinear Analysis TheoryMethods amp Applications vol 71 no 12 pp e1337ndashe1343 2009

[44] R Picard The Economics and Financing of Media CompaniesFordham University Press 2002

[45] M R Caputo Foundations of Dynamic Economic Analysis Opti-mal Control Theory and Applications Cambridge UniversityPress 2005

[46] T A Weber Optimal Control Theory with Applications inEconomics The MIT Press Cambridge Mass USA 2011

[47] H Jenkins Fans Bloggers and Gamers Media Consumer in theDigital Age Routledge London UK 2007

[48] E Benecchi andCColapinto ldquoEngagingwithGlee Transmediastorytelling for a television in transitionrdquo in Proceedings ofthe 25th International Conference of Communication (BusinessModels for a Digital Economy The Value of Contents) 2010

[49] J-C Rochet and J Tirole ldquoPlatform competition in two-sidedmarketsrdquo Journal of the European Economic Association vol 1no 4 pp 990ndash1029 2003

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Abstract and Applied Analysis 3

3 Popularity of TV Series A Dynamic Model

Connected marketing is used to underpin the popularity of abrand or a productThe success is affected by the capability ofgenerating engagement with customers and the engagementis relevant if we consider media content

From now on let 119875(119905) be a time dependent variablewhich describes the degree of popularity of a given productat the time 119905 We now formulate a model (similar modelshave been used in different contexts such as economicgrowth population dynamics and technology diffusion)which describes the behaviour of119875 over time and allows us todraw long run analysis We consider a local analysis in otherwords the diffusion path occurring in a specific country Weassume that popularity is driven by the following differentialequation

119889119875 (119905)

119889119905

= (120578 minus 120575) 119875 (119905) + 120591(1)

where

(i) 120575 is the natural depreciation rate (0 lt 120575 lt 1) ofpopularity Every product or service has a life cycleand when the market is mature it enters the declinestage and may die This term is also linked to thecultural discount [28] that is a particular program isrooted in one culture and thus is attractive in thatenvironment whilst it shall have diminished appealelsewhere The higher the cultural discount is thehigher the depreciation rate is

(ii) 120578 describes the actionsmade by the decisionmaker tosupport the campaign and by the other customers tospread information concerning the product

(iii) 120591 is an exogenous factor which takes into accountthe influence of the popularity of the product abroadA negative value means that the product failed in aforeign market and had a bad reputation which canaffect the campaign in the country under analysis Apositive value represents the success of the productor service abroad which can be translated in positivenetwork externalities in the country under analysisEven if it is a local model we have to consider theeffects derived from information flows and the trackrecords of the product elsewhere

It is possible to show that model (1) admits a solution of theform (120578 = 120575)

119875 (119905) = (119875 (0) +

120591

120578 minus 120575

) 119890

(minus120575+120578)119905minus

120591

120578 minus 120575

(2)

This kind of dynamic model formulated in terms of differen-tial equation has been widely used in the economic and socialscience literature to describe the evolution of variables such asinnovation population and human capital (see for instance[29ndash32]) If 120578 = 120575 the above model (1) becomes trivial and itadmits either a constant solution or a linear behavior (120591 = 0or 120591 = 0 resp)

4 Model Discussion

In the following discussion we present for each possible solu-tion a set of cases that could represent a concrete occurrenceof the solution itself The examples we are providing areonly explanatory and limited to the field of American TVseries imported in Italy We decided to focus on AmericanTV series for different reasons First foreign TV series andespecially American ones have historically dominated theItalian television market This gave us a sample which wasinternally coherent but provided also awide set of cases to testour model with Since we are taking into consideration notonly marketing actions undertaken by the local networks inorder to support specific TV series but also cultural practicesand fan activities that helped even unsupported TV series togain strength in the local market the fact that a remarkablenumber of American TV series had successfully conqueredthe Italian public despite the inherent cultural differencesbetween those shows and the local audience strategic [33]was also an influential factor in choosing our sample

(A) 120591 = 0 and 120578 = 0 This is the case in which there is noinfluence from abroad and no actions are undertakenThe solution to (1) is given by 119875(119905) = 119875(0)119890minus120575119905 As aresult 119875 goes to zero in the long run (Figure 1) thepopularity tends naturally to fade away If the decisionmaker does not intervene the attention of consumerswill focus on something else

This was the typical case of American TV series boughtthrough an output deal where the Italian broadcasters agreedto buy everything a specificmajor produces for an establishedperiod of timeThis kind of blind agreement obviously leadsto the purchase of TV series that are not strategic or evenadapted to the broadcasting network entitled to air themIn many cases Italian TV channels used those ldquoresidualrdquoproducts to fill up the night schedule or the many ldquovoidrdquospaces of a full day schedule This meant that the popularityand ratings of the TV series abroad were not influential inchoosing the time slot in which the products were aired northe broadcasting network felt the need to promote or push theproduct inside the local market

One classic example of the case in which there is noinfluence from abroad and no actions is the prime timedrama Angel (1999) a spin-off of the more popular Buffy theVampire Slayers produced by Warner Bros and purchasedin Italy by Mediaset The TV series was broadcasted inItaly by the private channel Italia 1 which had been airingBuffy as well in the overnight programming and with anerratic schedule It must be said that the purchase of Angelwas a direct consequence of the previous purchase of Buffyand not a strategic choice and this explains the lack ofldquorespectrdquo for the product both in its airing strategy and inits adaptation In this case the popularity of the series abroadhad no influence in the marketing and distribution in Italyand the degree of popularity of the TV series in the localmarket faded away quickly despite the huge popularity ofits mother series Buffy in the same market The fact thatItalia 1 never invested in the promotion of Angel and didnot intend to profit from the popularity of the series abroad

4 Abstract and Applied Analysis

1

08

06

04

02

0

P

0 20 40 60 80 100

t

Figure 1 Popularity fades away

ignoring it instead was crucial to the lack of success of theseries the airing of which was stopped after the third seasondespite that there were other two seasons to go before theproduction was stopped This is even clearer now since thesameTV series has been aired by the digital channel Rai4withdiscrete success Indeed the airing of American TV series ina new uncensored version and in day-time was crucial tothe success of the digital channel which reached a share of130 on the national level in 2009 ranking third among themost viewed national channels digitally broadcasted (Auditeldata season 2009 34) The promotion of Angel proposed byRai4 was aimed at profiting from its international ldquocult statusrdquoand underling strategic importance of the TV series for thedigital channel itself Headlines such as ldquofor the first time inprime timerdquo and ldquothe cult series in a new version only onRAI4rdquowere used among others to sustain those promotionalideas The launch was backed by serial fans on their blogs(see fi httpantoniogennawordpresscom20090528tv-)dig-angel-arriva-su-rai-4) Moreover Rai4 bets on interac-tivity and digital communication and has also Facebook andTwitter accounts in order to discuss with viewers

Another example is the American TV drama Supernat-ural Since its first airing on 13th September 2005 the CWprime time TV show became a fan favourite as acknowl-edged by TV critics and fandom experts [34ndash36] Despite aldquorabid fan followingrdquo and the identification of ldquocult showrdquoSupernatural was never a hit show What is relevant to thisstudy is that theCWhas never highly promoted Supernaturalsince the WB and UPN merged into the new network backin 2006 in comparison with its other prime time series Thelow promotion was combined during the 7 years of airingwith a schedule hopping from Tuesday toThursday to FridayThis fact was admitted in official statements by the CW com-munication executives who justified the lack of promotionwith the acknowledgment that Supernatural was considereda ldquoproven veteranrdquo that had already established itself andshould allow newcomers to ldquogain additional exposurerdquo [37]

Nevertheless the lack of promotion by the CW could beaccording to our model one of the reasons for the deceasingratings for the show Interestingly the same treatment in termof lack of promotion and erratic scheduling has been givento Supernatural in its Italian adaptation (see Section 41)

(B) 120591 = 0 and 120578 = 0 We assume that the actions dependon the degree of popularity and that the trend is linearThis approach is quite similar to the viral equationused by many researchers In this case the solution is119875(119905) = 119875(0)119890

(120578minus120575)119905 and two scenarios can happen

(a) If 120578 gt 120575 then 119875 will increase providing asuccessful campaign

The first five years ofThe Bold and the Beautiful (1987) in USwere not a good start for the CBS soap it was in fact thenetworkrsquos lowest-rated soap In this case though the aim ofthe producers was to create an international success and nota national one In fact since its first airing the soap has becomethe most-watched soap in the world with an audience of anestimated 262 million viewers [37] In Italy the investmentmade on the soap simply known as Beautiful was huge interms of promotion and distribution since the beginning ofits airing in 1990The soapwas scheduled in a crucial daytimetimeslot (1345) on Raidue and later on even in prime timewith a rhythm of 3 episodes per night In 1994 the soapwas bought by Mediaset but the daytime slot remained thesame even when the series started its airing on Canale5This was a crucial point in the promotional campaign whichstated that ldquothe lunch time is always beautifulrdquo stating thehappy marriage between Beautiful and the 1340 time slotThe faithfulness of the Italian audience toward the soap wasbuilt over time and based on the strategic scheduling thecollaboration between the American producers andMediasetgroup which lead to the setting of many storylines in Italy(f i Venezia 1997 Como 2000 and Portofino 2007) theinvestments in the promotional area that lead to localizedpromos with the leading actors and frequent visits from thecast in Italian talk shows and entertainment programs (lastof which was the participation of Ronn Moss the leadingmale actor in the Dancing with the stars Italian edition)and the investments in the distribution area with specialedition DVD sold in kiosks specialized volumes publishedby Mediaset Group and a reair of the daytime episodes inprime time on Mediaset digital platforms (La5 channel) Theratings for the American soap reflected its popularity in Italywith episodes reaching the record of 7 million viewers anda 37 share and more than 400 episodes with 6 millionof viewers each (Auditel data 34) Interesting enough theinternational success in this case reverberated on the originalcountry of production in two ways for once the soap waskept under production because of the selling power registeredabroad secondly the popularity of the show abroad seemedto affect the national audiences and by the mid-to-late 1990sthe numbers of the soap begun to climb and in the 2000sconstantly held the second position in the Nielsen weeklyratings for daytime dramas

Abstract and Applied Analysis 5

(b) If 120578 lt 120575 the product is not able to gain attentionand in the long run people will forget it

Women Murders Club a legal drama which ran on ABCfrom October 12 2007 to May 13 2008 was affected by the20072008 Writers Guild of America and by the subsequenterratic programming after the first 10 episodes were airedpeople had to wait 4 months to see the last 3 episodes theshow was also put in the Friday night prime time slot whichis considered a ldquodeath slotrdquo due to the concept that manyshows scheduled on or moved to Friday nights would not lastlong before cancellation due to low ratings From a receptionpoint of view not only the ratings were low (first seasonranked 57th with a medium of 8964m viewers) but alsothe critical response was tepid with Goodman [38] the SanFrancisco Chronicle TV critic publishing a highly criticalreview assigning the paperrsquos lowest possible rating and theNew York Times TV critic Stanley describing the show as ldquoallright but not good enoughrdquo [39] In fact Women MurdersClubwas cancelled onMay 12 2008 Mediaset had purchasedthe drama series before the strike judging just from the pilotand could not of course forecast the damages the strike wouldhave had on the development and even the ratings of manyAmerican TV showsWomenMurders Club suddenly becamean unwanted product because of the fast cancellation and thelack of popularity in the original country Mediaset ran theTV series first on the digital channel Joy part of its PremiumGallery and later because of the general lack of attentiondecides to use it to fill up the prime time slot of Canale5during the summer of 2010 The choice of programming anew drama series outside the guarantee period (11 Januaryndash30 June) is unusual but wise in this case the tepid receptionof the TV series first run both in US and in Italy the lack ofa previous successful campaign and of previous good resultsto build from and the small number of episodes availableconvinced the network that the series could not be consideredstrategic despite the fact that it was consistent to the channelidentity and target Women Murders Club is then offered tothe summer audience as a gift with a promotion built aroundits unusual scheduling (ldquoCanale5 offers you something neweven if it is Summerrdquo) and its resemblance to more populardramas (ldquoA mix between CSI Sex and The City and GreyrsquosAnatomyrdquo) The series is then used up as fast as possible inthe first week 4 episodes are aired in two nights (Tuesday andThursday) and from the second week the series is aired witha rhythm of 2 episodes per night on Thursday After a goodstart (1472 share and winner of the prime time) the ratingsdrop down week after week and the TV series is constantlysurpassed by old episodes of the scientific program Quarkaired by RAI in the same timeslot

(C) 120591 = 0 Under these hypotheses the solution is 119875(119905) =(119875(0)+120591(120578minus120575))119890

(120578minus120575)119905minus120591(120578minus120575) Different scenarios

can occur

(a) If 120578 gt 120575 then 119875 will increase providing asuccessful campaign whatever is the influencefrom abroad great investments in creating a

fandom would overturn the performance anddecrease the effects of bad reputation

The TV series Tequila and Bonetti (1992) inspired by themore popular movie Turner and Hooch (1989) starring TomHanks was aired by CBS from January 17th to April 18th1992 The detective comedy series was not a very successfulone and was cancelled after only 12 episodes Despite thatit proved to be a perfect match for the Italian channelItalia1 which aired the series repeatedly during the 1990sThe popularity of the TV series remained stable even aftermany years had passed since its last airing so much thatRete4 (Mediaset Group) started airing the TV series againin November 2009 What is even more interesting is thatafter 8 years from its cancellation in US a new season ofthe TV series was produced in Italy under the new title ofTequilaampBonetti (MastrofilmMediaTradeColumbia TriStarInternational Television 2000) Promotion and localizationof the series (Nick Bonetti was ldquotransferredrdquo in Rome andpartnered with an Italian celebrity in her first acting role)were independent from the American production and dis-tribution so much that the original producer Don Bellisarioonly discovered the existence of this second series years afterits first airing in Italy with obvious consequent legal issuesThe ldquolocalizedrdquo second season of the original American serieswas gifted with similar success and the 22 episodes airedrepeatedly on Italia1 and later on the satellite channels SkyShow (2008) and Sky Uno (2009) In this case the investmentin the promotion and adaptation of the TV series was hugedespite the lack of success of the product in the originalcountry of production

(b) If 120578 lt 120575 the popularity will tend to minus120591(120578minus120575) Inthis case the reputation and popularity abroadreally drive the internal performance

(b1) If 120591 is positive then the long run results ofthe campaign will end up in a success casewhose intensity is proportional to 120591

In this case the popularity of the TV series in the local marketis connected with the popularity of the TV series abroad CSIMiami (2002) the first spin-off of the forensic drama CSIarrived in Italy at the end of 2003 after the huge successregistered by the original CSI on the channel Italia1 and theevenmore huge success of the show in the worldwidemarketIt was not necessary to build up a big promotional campaignfor the TV series because the international success of the CSIfranchise was speaking for itself Later on CSI Miami waseven named the most popular program in the world becauseit featured in more countriesrsquo top 10 rankings for 2005 thanany other [40] and this data was used in the Italian promosfor the show Building from the international success of thefranchise and of the TV series itself CSI Miami soon becameone of themost viewed programs ofWednesday night and themost viewed series between the CSI franchises in Italy Theconfidence in the Italian success of CSI Miami is so strongthat in 2006 the series was even used to counterbalance theflop of the third season of The OC replacing the teen dramaon Sunday night and airing twice a week for months

6 Abstract and Applied Analysis

(b2) If 120591 is negative the fail in the foreign coun-tries will imply a decreasing popularity andeven worse the creation of people spreadingnegative comments on the product

This was the case of Defying Gravity a multinationallyproduced space travel drama which first aired on ABCin August 2009 The low ratings convinced the Americannetwork to suspend the series even if only 8 episodes outof the 13 produced had been aired When the debacle of theseries abroad was clear the Italian satellite channel Sky hadalready purchased the full first season and decided to air theproduct anyway on Fox Life starting 12 June 2010 in the lateprime time-slot (2155) The promotion and distribution ofthe show could not in this case profit from the internationalsuccess and had instead to fight against the bad popularity ofthe TV series which was even more evident because of thehigh profile promotion made in the original countryDefyingGravitywas in fact supposed to have 6 seasons 6 years was infact the length of the interplanetary voyage which plannedto visit most of the planets of the Solar System and wasmarketed as ldquoa Greyrsquos anatomy set in spacerdquo establishing adirect link with the most successful medical drama of ABCand playing with the fact that the two series had the sameproducing teamThis kind of promotionmade the seriesrsquo flopevenmore problematic for the international broadcasters Skyreused the ABC reference to Greyrsquos Anatomy a huge successin the Italianmarket too but tried to obscure any reference tosci-fi selling the show as a soap and adding to the main titlethe subtitle ldquothe galaxy of heartsrdquo The choice of schedulingDefying Gravity on Fox Lifemdashdedicated to family dramaand medicalsmdashand the late night summer slot-time thoughwere clear indications that the product was not consideredstrategic anymore because of the bad reputation it had gainedabroad

If 120578 = 0 then the popularity will tend to 120591120575 Thisis the case in Italy of the Law and Order franchise (1990)the success (120591 gt 0) of which is obviously disconnectedfrom the amount of local investments the dedication of thebroadcasting networks in the promotion and distributionarea for the single series in fact has always tended to zero inItaly This is shown by the small number of promos realizedfor each series all through their airing by the scheduling ofall the series in the late night or even in the night-time slotsand by the fact that they have been running both on RAIand Mediaset channels with no intention of connecting thesingle series to the specific channels Law and Order SVU forinstance has been used by Rete4 to fill up void spaces in thelate night schedule (between October and November 200710 out of the 22 episodes of the first season were aired inno particular order) before becoming the regular fill for thelate night time slot of the channel Law and Order timesloton Raidue often changed from daytime to late night andback again depending on the nature of the single episodewhile the 17th season (last one of the original series) has beenmoved to the prime time of Raitre Despite all the changes andlack of promotion the constant popularity of the TV seriesabroad and the strong niche following in Italy has made of

02468101214161820

0 20 40 60 80 100

times105

Figure 2 Popularity of Supernatural fades away

the Law and Order franchise a reliable show with specialregards to the ratings which remain constant

41 An Empirical Evidence As mention above in ItalySupernaturalrsquos performance has been affected by the lack of(or scarce) promotion and erratic scheduling (in particularshifting from springtime to summer a season characterizedby lower audience data)

Figure 2 shows the Auditel data [41] of the first four seriesof Supernatural broadcast on Rai2 channel in the period2007ndash2010 in detail the first season was broadcast duringFebruary-July 2007 the second June-September 2008 thethird July-September 2009 and the fourth July-August 2010The x axis shows the sequence of episodes whilst the y axislists the corresponding audience data

Figure 2 suggests that there are fluctuations of the dataaround the black trend line whose intensity is decreasingover time However Supernaturalrsquos long-run behavior can bewell approximated by the function 119875(119905) = 106119890minus0013119905 thatshows an exponential decay of popularity In particular thisempirical evidence shows that 120578 minus 120575 = minus0013 that is 120578 lt 120575implying that either 120578 = 0 (lack of promotion) or nonzero120578 lt 120575 (scarse promotion)

The parametric estimation has been done using thetechnique presented in [42 43] and based on the solution ofan inverse problem for a differential equation

5 An Optimal Decision ModelThe Decision Maker View Point

In a media company the decision maker faces the problemof maximizing profits subject to some constraints Mediacompanies must cover their costs (license fees productioncosts of programs ) and create returns just as any otherbusiness [44]The above formulatedmodel is purely dynamicand that does not provide any optimal decision rule Thepurpose of this section is indeed to formulate a dynamicprogramming model that can fully describe the complexityof a decision making process [45 46] We assume we havea closed market in which there is no influence of thepopularity of the product abroad and then 120591 is assumed to be

Abstract and Applied Analysis 7

zero With respect to the purely dynamic model previouslydescribed in which the term 120578 was supposed to be constantin this context we assume that 120578(119875(119905)) = Ω119875(119905) minus 120587(119905) whereΩ119875(119905) represents the revenues (depending on the level ofpopularity) that a TV company receives from the sale of adspaces to advertisers (Ω can be interpreted as the price of adspace) while 120587(119905) are the profits to be maximized by the DM

The difference Ω119875(119905) minus 120587(119905) is the investment in amarketing campaign The DM tries to maximize hisherintertemporal utility subject to a dynamic constraint thatdescribes the evolution of popularity and it can be formulatedas follows

Max int+infin

0

119880 (120587 (119905)) 119890

minus120588119905119889119905

st 119889119875 (119905)119889119905

= (minus120575 + Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

119875 (0) = 1198750

(3)

where 120588 is the discount rateThe variable 119875(119905) is the state variable while 120587(119905) is the

control For simplicity we assume a logarithmic utility119880 thatis 119880(120587(119905)) = ln(120587(119905)) even if other utility expressions couldbe considered analogously The following result states theexistence of a nontrivial equilibrium for the above dynamicmodel

Proposition 1 Suppose 120588 gt 120575 Then the above model showsthe existence of a nonzero equilibrium (119875lowast 120587lowast) where

119875

lowast=

120588

Ω

120587

lowast= 120588 minus 120575

(4)

Proof It is provided in the Appendix

In other words if the technical condition 120588 gt 120575 issatisfied this dynamic model shows the existence of a non-trivial equilibrium (119875lowast 120587lowast)The equilibrium of popularity119875lowastdepends on the price Ω and the higher will be the cost of amedia product for a customer the lower will be the level of119875lowastHowever as the analytical discussion in the Appendix showsthis equilibrium is unstable this practically means that onlyunder strict conditions the popularity will not vanish in thelong run

6 Conclusions

Internet provides tools that can alter the whole experienceof watching television giving access to the process not justthe results Through online communities in fact passionateviewers find and share a privileged knowledge which isderived both from the viewing experience and the extratex-tual elements of the show [21] According to recent studiesfans aremaking a new kind of television scene that transcendsplace and shakes up long-standing balances of power betweenfans and the television makers In general the most recentliterature published in the field of fan studies suggests that

the line between consumption and production is blurringinto a new paradigm with fans growing up to be creators andcreators trying to connect and engage with fan communitieswhen not labeling themselves as fans [13 21 47]

Themost successful TV series analyzed in this study havein fact been created promoted and distributed not onlytaking into account the existence of an active and internet-based fan audience but also relying on this same audience inorder to make the series an international success Comparedwith the ones that did not profit from the presence of afan audience or did not use connected marketing strategiesthese TV series have indeed succeeded in generating deepperpetual audience engagement

From a previous desk research and exploratory analysis[48] it emerged in fact that (a) there is a willingness toconsume texts offered by producers in different formatsoutside of the narrative space of the show itself and (b) partof the reason for this extratextual success lies in the initialconstruction and marketing of the show itself

Building from these results the model we propose heretries to identify and explain the main factors on whichthe popularity of American TV series in Italy is basedAll the examples confirm in fact the relevance of collateralactions specifically web orientated to underpin the successof televisionrsquos content as well as the influence of foreign popu-larity (globalization) which can be considered the explainingvariable involved in the success of a media product

The paper also introduces a decisional dynamic modelable to sustain the DM in hisher decisions In the Italianscenario commercial television plays a predominant role andcompetes to attract viewersrsquo attention and then sells thatattention to advertisers [49] In other words a broadcastingmedia platform can only succeed if it has viewers otherwiseits revenues from advertising would be zero As it is anadvertisement-supportedmedia from the two-sidedmarketsliterature we know that ad prices reflect both the value ofreaching a given audience and the marginal effect of theadvertisement sale on total audience size Thus popular TVprograms indirectly generate returns for a media companyattracting viewers Our model provides the DM the optimalsolution balancing the investment in sustaining programpopularity and the maximization of profits

For future works we aim at modifying this model byintroducing a stochastic term able to catch the naturalfluctuations arising from audience data

Appendix

In an optimal decision making process the DM tries to solvethe following model

Max int+infin

0

ln (120587 (119905)) 119890minus120588119905119889119905

st 119889119875 (119905)119889119905

= (minus120575 + Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

119875 (0) = 1198750

(5)

8 Abstract and Applied Analysis

The Hamiltonian associated with model (5) is

119867(119875 (119905) 120587 (119905)) = ln (120587 (119905)) 119890minus120588119905 + 120582 (119905)

times (minus120575119875 (119905) + (Ω119875 (119905) minus 120587 (119905)) 119875 (119905))

(6)

Optimality conditions for (6) read as

0 =

120597119867

120597120587

=

119890

minus120588119905

120587 (119905)

minus 120582 (119905) 119875 (119905)

minus

120582 (119905) =

120597119867

120597119875

= 120582 (119905) (minus120575 + 2Ω119875 (119905) minus 120587 (119905))

119875 (119905) =

120597119867

120597120582

= minus120575119875 (119905) + (Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

(7)

The system (7) is equivalent to

120587 (119905) =

119890

minus120588119905

120582 (119905) 119875 (119905)

997904rArr

(119905)

120587 (119905)

= minus120588 minus

120582 (119905)

120582 (119905)

minus

119875 (119905)

119875 (119905)

minus

120582 (119905) = 120582 (119905) (minus120575 + 2Ω119875 (119905) minus 120587 (119905))

997904rArr minus

120582 (119905)

120582 (119905)

= minus120575 + 2Ω119875 (119905) minus 120587 (119905)

119875 (119905) = minus120575119875 (119905) + (Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

997904rArr

119875 (119905)

119875 (119905)

= minus120575 + Ω119875 (119905) minus 120587 (119905)

(8)

which implies

(119905)

120587 (119905)

= minus120588 + Ω119875 (119905)

119875 (119905)

119875 (119905)

= minus120575 + Ω119875 (119905) minus 120587 (119905)

(9)

The only nontrivial equilibrium is

119875

lowast=

120588

Ω

120587

lowast= 120588 minus 120575 gt 0

(10)

The Jacobian of the linearized system at (119875lowast 120587lowast) is equal to

119869 = [

0 Ω (120588 minus 120575)

minus

120588

Ω

120588

] (11)

The determinant of 119869 is equal to

det (119869) = 120588 (120588 minus 120575) gt 0 (12)

while the trace of 119869 is equal to

trace (119869) = 120588 gt 0 (13)

which implies that (119875lowast 120587lowast) is an unstable equilibrium Itis possible to show that this system admits three moreequilibria namely (0 0) (119875lowast 0) and (0 120587lowast) Among them(0 0) and (0 120587lowast) are locally asymptotically stable

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] C Colapinto ldquoMoving to a multichannel and multiplatformcompany in the emerging and digital media ecosystem the caseof mediaset grouprdquo International Journal on Media Manage-ment vol 12 no 2 pp 59ndash75 2010

[2] TWeinbergTheNewCommunity RulesMarketing on the SocialWeb OrsquoReilly Media Inc Sebastopol Calif USA 2009

[3] C Colapinto and E Benecchi ldquoMovie industry goes viral inthe XXIst century if what counts is the buzzrdquo in CrossmediaInnovations I Ibrus and C A Scolari Eds pp 161ndash178 PeterLang Berlin Germany 2012

[4] C Colapinto and E Benecchi ldquoThe presentation of celebritypersonas in everyday twittering managing online reputationsthroughout a communication crisisrdquo Media Culture amp Societyvol 36 pp 219ndash233 2014

[5] A Toffler Future Shock William Morrow and Company NewYork NY USA 1980

[6] L Kung Strategic Management in the Media SAGE LondonUK 2008

[7] M PMcAllister and J Turrow ldquoNewmedia and the commercialsphere two intersecting trends five categories of concernrdquoJournal of Broadcasting amp Electronic Media vol 46 no 4 pp505ndash514 2002

[8] W S McDowell ldquoIssues in Marketing and Brandingrdquo in Hand-book of Media Management and Economics A B Albarran SM Chan-Olmsted and M O Wirth Eds pp 229ndash250 LEANew Jersey NJ USA 2006

[9] E Katz and P F Lazarsfeld Personal Influence The Free PressNew York NY USA 1955

[10] R Ando and A Marinelli ldquoFare ricerca sul fandom on line Ifan italiani e le serie tvrdquo in Sociologia 20 Pratiche Sociali eMetodologie di Ricerca sui Media Partecipativi S Monaci andB Scifo Eds 2010 Scriptaweb httpscriptawebeuCatalogosociologia-2-0

[11] A de Kosnik ldquoShould fan fiction be freerdquo Cinema Journal vol48 no 4 pp 118ndash124 2009

[12] C Sandvoss Fans Polity Press Cambridge UK 2005[13] I Askwith TV 20 turning television into an engagement

medium [MS thesis] 2007 httpcmsmiteduresearchthesesIvanAskwith2007pdf

[14] P BoothDigital Fandom NewMedia Studies Peter Lung 2010[15] J Caldwell ldquoCritical industrial practice branding repurposing

and the migratory patterns of the industrial textsrdquo Television ampNew Media vol 7 pp 99ndash104 2006

[16] H Jenkins S Ford and J Green Spreadable Media NYU NewYork NY USA 2013

[17] E Benecchi and G Richeri ldquoTv to talk about engaging withAmerican tv series through the internetrdquo inThe New TelevisionEcosystem A Abbruzzese and L Fortunato Eds Peter LangBern Switzerland 2013

[18] J T Caldwell Production Culture Duke University PressDurham NC USA 2008

[19] H Jenkins Convergence Culture Where Old and New MediaCollide New York University Press New York NY USA 2006

Abstract and Applied Analysis 9

[20] M Hills Fan Cultures Routledge London UK 2003[21] N Baym Personal Connections in the Digital Age Polity Press

Cambridge UK 2000[22] I Condry ldquoCultures of music piracy an ethnographic com-

parison of the US and Japanrdquo International Journal of CulturalStudies vol 7 pp 343ndash363 2004

[23] AAustinH Jenkins J Green I Askwith and S Ford ldquoTurningpirates into loyalists the moral economy and an alternativeresponse to file sharingrdquo Tech Rep MIT Convergence CultureConsortium Cambridge UK 2006

[24] D Boyd Facebookrsquos Little Gifts Apophenia 2007[25] H Jenkins ldquoLook ListenWalk Technologyrdquo 2004 httpwww

technologyreviewcomInfoTechwtr 13560[26] M Scaglioni TV di culto La Serialita Televisiva Americana e il

Suo Fandom Vita e Pensiero Milano Italy 2006[27] L Porter and D Lavery ldquoCultivating a lost audience the part-

icipatory fan culture of lostrdquo in Unlocking the Meaning ofLost An Unauthorized Guide L Porter and D Lavery EdsSourcebooks Naperville Ill USA 2006

[28] C Hoskins and R Mirus ldquoReasons for the US dominanceof the international trade in television programmesrdquo MediaCulture and Society vol 10 pp 499ndash515 1988

[29] C Colapinto E Sartori andM Tolotti ldquoAwareness persuasionand adoption enriching the bassmodelrdquo Physica A vol 395 pp1ndash10 2014

[30] A Bucci C Colapinto M Forster and D la Torre ldquoStochastictechnology shocks in an extended Uzawa-Lucas model closed-form solution and long-run dynamicsrdquo Journal of EconomicsZeitschrift fur Nationalokonomie vol 103 no 1 pp 83ndash99 2011

[31] V Capasso R Engbers and D la Torre ldquoOn a spatial Solowmodel with technological diffusion and nonconcave productionfunctionrdquo Nonlinear Analysis Real World Applications vol 11no 5 pp 3858ndash3876 2010

[32] D la Torre and S Marsiglio ldquoEndogenous technologicalprogress in a multi-sector growth modelrdquo Economic Modellingvol 27 no 5 pp 1017ndash1028 2010

[33] D Bielby and C HarringtonGlobal TV NYU Press New YorkNY USA 2008

[34] C Tosenberger ldquoSaving people hunting thingsrdquo TransformativeWorks and Culture vol 4 2010

[35] H Jenkins ldquoSupernatural first impressionsrdquo Confessions of anACA-fan 2007 httphenryjenkinsorg200701supernaturalhtml

[36] L Zubernis and K Larsen Eds Fan Phenomena SupernaturalIntellect Books Bristol UK 2014

[37] M Wilson ldquoCW Exec Professes Support for Supernaturalrdquo2008 httpscifiaboutcomb20080122cw-exec-professes-support-for-supernaturalhtm

[38] T Goodman ldquoWomenrsquosMurder Club-bonding over crimerdquo SanFrancisco Chronicle October 2007

[39] A Stanley ldquoHomicide and Heelsrdquo The New York TimesOctober 2007

[40] Informa Telecoms and Media ldquoWorld most popular showsrdquoRadio Times August 2006

[41] ldquoAuditel datardquo httpwwwauditelit[42] H E Kunze D la Torre and E R Vrscay ldquoInverse problems

for random differential equations using the collage method forrandom contraction mappingsrdquo Journal of Computational andApplied Mathematics vol 223 no 2 pp 853ndash861 2009

[43] H Kunze D la Torre and E R Vrscay ldquoA generalized collagemethod based upon the Lax-Milgram functional for solvingboundary value inverse problemsrdquo Nonlinear Analysis TheoryMethods amp Applications vol 71 no 12 pp e1337ndashe1343 2009

[44] R Picard The Economics and Financing of Media CompaniesFordham University Press 2002

[45] M R Caputo Foundations of Dynamic Economic Analysis Opti-mal Control Theory and Applications Cambridge UniversityPress 2005

[46] T A Weber Optimal Control Theory with Applications inEconomics The MIT Press Cambridge Mass USA 2011

[47] H Jenkins Fans Bloggers and Gamers Media Consumer in theDigital Age Routledge London UK 2007

[48] E Benecchi andCColapinto ldquoEngagingwithGlee Transmediastorytelling for a television in transitionrdquo in Proceedings ofthe 25th International Conference of Communication (BusinessModels for a Digital Economy The Value of Contents) 2010

[49] J-C Rochet and J Tirole ldquoPlatform competition in two-sidedmarketsrdquo Journal of the European Economic Association vol 1no 4 pp 990ndash1029 2003

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Abstract and Applied Analysis

1

08

06

04

02

0

P

0 20 40 60 80 100

t

Figure 1 Popularity fades away

ignoring it instead was crucial to the lack of success of theseries the airing of which was stopped after the third seasondespite that there were other two seasons to go before theproduction was stopped This is even clearer now since thesameTV series has been aired by the digital channel Rai4withdiscrete success Indeed the airing of American TV series ina new uncensored version and in day-time was crucial tothe success of the digital channel which reached a share of130 on the national level in 2009 ranking third among themost viewed national channels digitally broadcasted (Auditeldata season 2009 34) The promotion of Angel proposed byRai4 was aimed at profiting from its international ldquocult statusrdquoand underling strategic importance of the TV series for thedigital channel itself Headlines such as ldquofor the first time inprime timerdquo and ldquothe cult series in a new version only onRAI4rdquowere used among others to sustain those promotionalideas The launch was backed by serial fans on their blogs(see fi httpantoniogennawordpresscom20090528tv-)dig-angel-arriva-su-rai-4) Moreover Rai4 bets on interac-tivity and digital communication and has also Facebook andTwitter accounts in order to discuss with viewers

Another example is the American TV drama Supernat-ural Since its first airing on 13th September 2005 the CWprime time TV show became a fan favourite as acknowl-edged by TV critics and fandom experts [34ndash36] Despite aldquorabid fan followingrdquo and the identification of ldquocult showrdquoSupernatural was never a hit show What is relevant to thisstudy is that theCWhas never highly promoted Supernaturalsince the WB and UPN merged into the new network backin 2006 in comparison with its other prime time series Thelow promotion was combined during the 7 years of airingwith a schedule hopping from Tuesday toThursday to FridayThis fact was admitted in official statements by the CW com-munication executives who justified the lack of promotionwith the acknowledgment that Supernatural was considereda ldquoproven veteranrdquo that had already established itself andshould allow newcomers to ldquogain additional exposurerdquo [37]

Nevertheless the lack of promotion by the CW could beaccording to our model one of the reasons for the deceasingratings for the show Interestingly the same treatment in termof lack of promotion and erratic scheduling has been givento Supernatural in its Italian adaptation (see Section 41)

(B) 120591 = 0 and 120578 = 0 We assume that the actions dependon the degree of popularity and that the trend is linearThis approach is quite similar to the viral equationused by many researchers In this case the solution is119875(119905) = 119875(0)119890

(120578minus120575)119905 and two scenarios can happen

(a) If 120578 gt 120575 then 119875 will increase providing asuccessful campaign

The first five years ofThe Bold and the Beautiful (1987) in USwere not a good start for the CBS soap it was in fact thenetworkrsquos lowest-rated soap In this case though the aim ofthe producers was to create an international success and nota national one In fact since its first airing the soap has becomethe most-watched soap in the world with an audience of anestimated 262 million viewers [37] In Italy the investmentmade on the soap simply known as Beautiful was huge interms of promotion and distribution since the beginning ofits airing in 1990The soapwas scheduled in a crucial daytimetimeslot (1345) on Raidue and later on even in prime timewith a rhythm of 3 episodes per night In 1994 the soapwas bought by Mediaset but the daytime slot remained thesame even when the series started its airing on Canale5This was a crucial point in the promotional campaign whichstated that ldquothe lunch time is always beautifulrdquo stating thehappy marriage between Beautiful and the 1340 time slotThe faithfulness of the Italian audience toward the soap wasbuilt over time and based on the strategic scheduling thecollaboration between the American producers andMediasetgroup which lead to the setting of many storylines in Italy(f i Venezia 1997 Como 2000 and Portofino 2007) theinvestments in the promotional area that lead to localizedpromos with the leading actors and frequent visits from thecast in Italian talk shows and entertainment programs (lastof which was the participation of Ronn Moss the leadingmale actor in the Dancing with the stars Italian edition)and the investments in the distribution area with specialedition DVD sold in kiosks specialized volumes publishedby Mediaset Group and a reair of the daytime episodes inprime time on Mediaset digital platforms (La5 channel) Theratings for the American soap reflected its popularity in Italywith episodes reaching the record of 7 million viewers anda 37 share and more than 400 episodes with 6 millionof viewers each (Auditel data 34) Interesting enough theinternational success in this case reverberated on the originalcountry of production in two ways for once the soap waskept under production because of the selling power registeredabroad secondly the popularity of the show abroad seemedto affect the national audiences and by the mid-to-late 1990sthe numbers of the soap begun to climb and in the 2000sconstantly held the second position in the Nielsen weeklyratings for daytime dramas

Abstract and Applied Analysis 5

(b) If 120578 lt 120575 the product is not able to gain attentionand in the long run people will forget it

Women Murders Club a legal drama which ran on ABCfrom October 12 2007 to May 13 2008 was affected by the20072008 Writers Guild of America and by the subsequenterratic programming after the first 10 episodes were airedpeople had to wait 4 months to see the last 3 episodes theshow was also put in the Friday night prime time slot whichis considered a ldquodeath slotrdquo due to the concept that manyshows scheduled on or moved to Friday nights would not lastlong before cancellation due to low ratings From a receptionpoint of view not only the ratings were low (first seasonranked 57th with a medium of 8964m viewers) but alsothe critical response was tepid with Goodman [38] the SanFrancisco Chronicle TV critic publishing a highly criticalreview assigning the paperrsquos lowest possible rating and theNew York Times TV critic Stanley describing the show as ldquoallright but not good enoughrdquo [39] In fact Women MurdersClubwas cancelled onMay 12 2008 Mediaset had purchasedthe drama series before the strike judging just from the pilotand could not of course forecast the damages the strike wouldhave had on the development and even the ratings of manyAmerican TV showsWomenMurders Club suddenly becamean unwanted product because of the fast cancellation and thelack of popularity in the original country Mediaset ran theTV series first on the digital channel Joy part of its PremiumGallery and later because of the general lack of attentiondecides to use it to fill up the prime time slot of Canale5during the summer of 2010 The choice of programming anew drama series outside the guarantee period (11 Januaryndash30 June) is unusual but wise in this case the tepid receptionof the TV series first run both in US and in Italy the lack ofa previous successful campaign and of previous good resultsto build from and the small number of episodes availableconvinced the network that the series could not be consideredstrategic despite the fact that it was consistent to the channelidentity and target Women Murders Club is then offered tothe summer audience as a gift with a promotion built aroundits unusual scheduling (ldquoCanale5 offers you something neweven if it is Summerrdquo) and its resemblance to more populardramas (ldquoA mix between CSI Sex and The City and GreyrsquosAnatomyrdquo) The series is then used up as fast as possible inthe first week 4 episodes are aired in two nights (Tuesday andThursday) and from the second week the series is aired witha rhythm of 2 episodes per night on Thursday After a goodstart (1472 share and winner of the prime time) the ratingsdrop down week after week and the TV series is constantlysurpassed by old episodes of the scientific program Quarkaired by RAI in the same timeslot

(C) 120591 = 0 Under these hypotheses the solution is 119875(119905) =(119875(0)+120591(120578minus120575))119890

(120578minus120575)119905minus120591(120578minus120575) Different scenarios

can occur

(a) If 120578 gt 120575 then 119875 will increase providing asuccessful campaign whatever is the influencefrom abroad great investments in creating a

fandom would overturn the performance anddecrease the effects of bad reputation

The TV series Tequila and Bonetti (1992) inspired by themore popular movie Turner and Hooch (1989) starring TomHanks was aired by CBS from January 17th to April 18th1992 The detective comedy series was not a very successfulone and was cancelled after only 12 episodes Despite thatit proved to be a perfect match for the Italian channelItalia1 which aired the series repeatedly during the 1990sThe popularity of the TV series remained stable even aftermany years had passed since its last airing so much thatRete4 (Mediaset Group) started airing the TV series againin November 2009 What is even more interesting is thatafter 8 years from its cancellation in US a new season ofthe TV series was produced in Italy under the new title ofTequilaampBonetti (MastrofilmMediaTradeColumbia TriStarInternational Television 2000) Promotion and localizationof the series (Nick Bonetti was ldquotransferredrdquo in Rome andpartnered with an Italian celebrity in her first acting role)were independent from the American production and dis-tribution so much that the original producer Don Bellisarioonly discovered the existence of this second series years afterits first airing in Italy with obvious consequent legal issuesThe ldquolocalizedrdquo second season of the original American serieswas gifted with similar success and the 22 episodes airedrepeatedly on Italia1 and later on the satellite channels SkyShow (2008) and Sky Uno (2009) In this case the investmentin the promotion and adaptation of the TV series was hugedespite the lack of success of the product in the originalcountry of production

(b) If 120578 lt 120575 the popularity will tend to minus120591(120578minus120575) Inthis case the reputation and popularity abroadreally drive the internal performance

(b1) If 120591 is positive then the long run results ofthe campaign will end up in a success casewhose intensity is proportional to 120591

In this case the popularity of the TV series in the local marketis connected with the popularity of the TV series abroad CSIMiami (2002) the first spin-off of the forensic drama CSIarrived in Italy at the end of 2003 after the huge successregistered by the original CSI on the channel Italia1 and theevenmore huge success of the show in the worldwidemarketIt was not necessary to build up a big promotional campaignfor the TV series because the international success of the CSIfranchise was speaking for itself Later on CSI Miami waseven named the most popular program in the world becauseit featured in more countriesrsquo top 10 rankings for 2005 thanany other [40] and this data was used in the Italian promosfor the show Building from the international success of thefranchise and of the TV series itself CSI Miami soon becameone of themost viewed programs ofWednesday night and themost viewed series between the CSI franchises in Italy Theconfidence in the Italian success of CSI Miami is so strongthat in 2006 the series was even used to counterbalance theflop of the third season of The OC replacing the teen dramaon Sunday night and airing twice a week for months

6 Abstract and Applied Analysis

(b2) If 120591 is negative the fail in the foreign coun-tries will imply a decreasing popularity andeven worse the creation of people spreadingnegative comments on the product

This was the case of Defying Gravity a multinationallyproduced space travel drama which first aired on ABCin August 2009 The low ratings convinced the Americannetwork to suspend the series even if only 8 episodes outof the 13 produced had been aired When the debacle of theseries abroad was clear the Italian satellite channel Sky hadalready purchased the full first season and decided to air theproduct anyway on Fox Life starting 12 June 2010 in the lateprime time-slot (2155) The promotion and distribution ofthe show could not in this case profit from the internationalsuccess and had instead to fight against the bad popularity ofthe TV series which was even more evident because of thehigh profile promotion made in the original countryDefyingGravitywas in fact supposed to have 6 seasons 6 years was infact the length of the interplanetary voyage which plannedto visit most of the planets of the Solar System and wasmarketed as ldquoa Greyrsquos anatomy set in spacerdquo establishing adirect link with the most successful medical drama of ABCand playing with the fact that the two series had the sameproducing teamThis kind of promotionmade the seriesrsquo flopevenmore problematic for the international broadcasters Skyreused the ABC reference to Greyrsquos Anatomy a huge successin the Italianmarket too but tried to obscure any reference tosci-fi selling the show as a soap and adding to the main titlethe subtitle ldquothe galaxy of heartsrdquo The choice of schedulingDefying Gravity on Fox Lifemdashdedicated to family dramaand medicalsmdashand the late night summer slot-time thoughwere clear indications that the product was not consideredstrategic anymore because of the bad reputation it had gainedabroad

If 120578 = 0 then the popularity will tend to 120591120575 Thisis the case in Italy of the Law and Order franchise (1990)the success (120591 gt 0) of which is obviously disconnectedfrom the amount of local investments the dedication of thebroadcasting networks in the promotion and distributionarea for the single series in fact has always tended to zero inItaly This is shown by the small number of promos realizedfor each series all through their airing by the scheduling ofall the series in the late night or even in the night-time slotsand by the fact that they have been running both on RAIand Mediaset channels with no intention of connecting thesingle series to the specific channels Law and Order SVU forinstance has been used by Rete4 to fill up void spaces in thelate night schedule (between October and November 200710 out of the 22 episodes of the first season were aired inno particular order) before becoming the regular fill for thelate night time slot of the channel Law and Order timesloton Raidue often changed from daytime to late night andback again depending on the nature of the single episodewhile the 17th season (last one of the original series) has beenmoved to the prime time of Raitre Despite all the changes andlack of promotion the constant popularity of the TV seriesabroad and the strong niche following in Italy has made of

02468101214161820

0 20 40 60 80 100

times105

Figure 2 Popularity of Supernatural fades away

the Law and Order franchise a reliable show with specialregards to the ratings which remain constant

41 An Empirical Evidence As mention above in ItalySupernaturalrsquos performance has been affected by the lack of(or scarce) promotion and erratic scheduling (in particularshifting from springtime to summer a season characterizedby lower audience data)

Figure 2 shows the Auditel data [41] of the first four seriesof Supernatural broadcast on Rai2 channel in the period2007ndash2010 in detail the first season was broadcast duringFebruary-July 2007 the second June-September 2008 thethird July-September 2009 and the fourth July-August 2010The x axis shows the sequence of episodes whilst the y axislists the corresponding audience data

Figure 2 suggests that there are fluctuations of the dataaround the black trend line whose intensity is decreasingover time However Supernaturalrsquos long-run behavior can bewell approximated by the function 119875(119905) = 106119890minus0013119905 thatshows an exponential decay of popularity In particular thisempirical evidence shows that 120578 minus 120575 = minus0013 that is 120578 lt 120575implying that either 120578 = 0 (lack of promotion) or nonzero120578 lt 120575 (scarse promotion)

The parametric estimation has been done using thetechnique presented in [42 43] and based on the solution ofan inverse problem for a differential equation

5 An Optimal Decision ModelThe Decision Maker View Point

In a media company the decision maker faces the problemof maximizing profits subject to some constraints Mediacompanies must cover their costs (license fees productioncosts of programs ) and create returns just as any otherbusiness [44]The above formulatedmodel is purely dynamicand that does not provide any optimal decision rule Thepurpose of this section is indeed to formulate a dynamicprogramming model that can fully describe the complexityof a decision making process [45 46] We assume we havea closed market in which there is no influence of thepopularity of the product abroad and then 120591 is assumed to be

Abstract and Applied Analysis 7

zero With respect to the purely dynamic model previouslydescribed in which the term 120578 was supposed to be constantin this context we assume that 120578(119875(119905)) = Ω119875(119905) minus 120587(119905) whereΩ119875(119905) represents the revenues (depending on the level ofpopularity) that a TV company receives from the sale of adspaces to advertisers (Ω can be interpreted as the price of adspace) while 120587(119905) are the profits to be maximized by the DM

The difference Ω119875(119905) minus 120587(119905) is the investment in amarketing campaign The DM tries to maximize hisherintertemporal utility subject to a dynamic constraint thatdescribes the evolution of popularity and it can be formulatedas follows

Max int+infin

0

119880 (120587 (119905)) 119890

minus120588119905119889119905

st 119889119875 (119905)119889119905

= (minus120575 + Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

119875 (0) = 1198750

(3)

where 120588 is the discount rateThe variable 119875(119905) is the state variable while 120587(119905) is the

control For simplicity we assume a logarithmic utility119880 thatis 119880(120587(119905)) = ln(120587(119905)) even if other utility expressions couldbe considered analogously The following result states theexistence of a nontrivial equilibrium for the above dynamicmodel

Proposition 1 Suppose 120588 gt 120575 Then the above model showsthe existence of a nonzero equilibrium (119875lowast 120587lowast) where

119875

lowast=

120588

Ω

120587

lowast= 120588 minus 120575

(4)

Proof It is provided in the Appendix

In other words if the technical condition 120588 gt 120575 issatisfied this dynamic model shows the existence of a non-trivial equilibrium (119875lowast 120587lowast)The equilibrium of popularity119875lowastdepends on the price Ω and the higher will be the cost of amedia product for a customer the lower will be the level of119875lowastHowever as the analytical discussion in the Appendix showsthis equilibrium is unstable this practically means that onlyunder strict conditions the popularity will not vanish in thelong run

6 Conclusions

Internet provides tools that can alter the whole experienceof watching television giving access to the process not justthe results Through online communities in fact passionateviewers find and share a privileged knowledge which isderived both from the viewing experience and the extratex-tual elements of the show [21] According to recent studiesfans aremaking a new kind of television scene that transcendsplace and shakes up long-standing balances of power betweenfans and the television makers In general the most recentliterature published in the field of fan studies suggests that

the line between consumption and production is blurringinto a new paradigm with fans growing up to be creators andcreators trying to connect and engage with fan communitieswhen not labeling themselves as fans [13 21 47]

Themost successful TV series analyzed in this study havein fact been created promoted and distributed not onlytaking into account the existence of an active and internet-based fan audience but also relying on this same audience inorder to make the series an international success Comparedwith the ones that did not profit from the presence of afan audience or did not use connected marketing strategiesthese TV series have indeed succeeded in generating deepperpetual audience engagement

From a previous desk research and exploratory analysis[48] it emerged in fact that (a) there is a willingness toconsume texts offered by producers in different formatsoutside of the narrative space of the show itself and (b) partof the reason for this extratextual success lies in the initialconstruction and marketing of the show itself

Building from these results the model we propose heretries to identify and explain the main factors on whichthe popularity of American TV series in Italy is basedAll the examples confirm in fact the relevance of collateralactions specifically web orientated to underpin the successof televisionrsquos content as well as the influence of foreign popu-larity (globalization) which can be considered the explainingvariable involved in the success of a media product

The paper also introduces a decisional dynamic modelable to sustain the DM in hisher decisions In the Italianscenario commercial television plays a predominant role andcompetes to attract viewersrsquo attention and then sells thatattention to advertisers [49] In other words a broadcastingmedia platform can only succeed if it has viewers otherwiseits revenues from advertising would be zero As it is anadvertisement-supportedmedia from the two-sidedmarketsliterature we know that ad prices reflect both the value ofreaching a given audience and the marginal effect of theadvertisement sale on total audience size Thus popular TVprograms indirectly generate returns for a media companyattracting viewers Our model provides the DM the optimalsolution balancing the investment in sustaining programpopularity and the maximization of profits

For future works we aim at modifying this model byintroducing a stochastic term able to catch the naturalfluctuations arising from audience data

Appendix

In an optimal decision making process the DM tries to solvethe following model

Max int+infin

0

ln (120587 (119905)) 119890minus120588119905119889119905

st 119889119875 (119905)119889119905

= (minus120575 + Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

119875 (0) = 1198750

(5)

8 Abstract and Applied Analysis

The Hamiltonian associated with model (5) is

119867(119875 (119905) 120587 (119905)) = ln (120587 (119905)) 119890minus120588119905 + 120582 (119905)

times (minus120575119875 (119905) + (Ω119875 (119905) minus 120587 (119905)) 119875 (119905))

(6)

Optimality conditions for (6) read as

0 =

120597119867

120597120587

=

119890

minus120588119905

120587 (119905)

minus 120582 (119905) 119875 (119905)

minus

120582 (119905) =

120597119867

120597119875

= 120582 (119905) (minus120575 + 2Ω119875 (119905) minus 120587 (119905))

119875 (119905) =

120597119867

120597120582

= minus120575119875 (119905) + (Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

(7)

The system (7) is equivalent to

120587 (119905) =

119890

minus120588119905

120582 (119905) 119875 (119905)

997904rArr

(119905)

120587 (119905)

= minus120588 minus

120582 (119905)

120582 (119905)

minus

119875 (119905)

119875 (119905)

minus

120582 (119905) = 120582 (119905) (minus120575 + 2Ω119875 (119905) minus 120587 (119905))

997904rArr minus

120582 (119905)

120582 (119905)

= minus120575 + 2Ω119875 (119905) minus 120587 (119905)

119875 (119905) = minus120575119875 (119905) + (Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

997904rArr

119875 (119905)

119875 (119905)

= minus120575 + Ω119875 (119905) minus 120587 (119905)

(8)

which implies

(119905)

120587 (119905)

= minus120588 + Ω119875 (119905)

119875 (119905)

119875 (119905)

= minus120575 + Ω119875 (119905) minus 120587 (119905)

(9)

The only nontrivial equilibrium is

119875

lowast=

120588

Ω

120587

lowast= 120588 minus 120575 gt 0

(10)

The Jacobian of the linearized system at (119875lowast 120587lowast) is equal to

119869 = [

0 Ω (120588 minus 120575)

minus

120588

Ω

120588

] (11)

The determinant of 119869 is equal to

det (119869) = 120588 (120588 minus 120575) gt 0 (12)

while the trace of 119869 is equal to

trace (119869) = 120588 gt 0 (13)

which implies that (119875lowast 120587lowast) is an unstable equilibrium Itis possible to show that this system admits three moreequilibria namely (0 0) (119875lowast 0) and (0 120587lowast) Among them(0 0) and (0 120587lowast) are locally asymptotically stable

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] C Colapinto ldquoMoving to a multichannel and multiplatformcompany in the emerging and digital media ecosystem the caseof mediaset grouprdquo International Journal on Media Manage-ment vol 12 no 2 pp 59ndash75 2010

[2] TWeinbergTheNewCommunity RulesMarketing on the SocialWeb OrsquoReilly Media Inc Sebastopol Calif USA 2009

[3] C Colapinto and E Benecchi ldquoMovie industry goes viral inthe XXIst century if what counts is the buzzrdquo in CrossmediaInnovations I Ibrus and C A Scolari Eds pp 161ndash178 PeterLang Berlin Germany 2012

[4] C Colapinto and E Benecchi ldquoThe presentation of celebritypersonas in everyday twittering managing online reputationsthroughout a communication crisisrdquo Media Culture amp Societyvol 36 pp 219ndash233 2014

[5] A Toffler Future Shock William Morrow and Company NewYork NY USA 1980

[6] L Kung Strategic Management in the Media SAGE LondonUK 2008

[7] M PMcAllister and J Turrow ldquoNewmedia and the commercialsphere two intersecting trends five categories of concernrdquoJournal of Broadcasting amp Electronic Media vol 46 no 4 pp505ndash514 2002

[8] W S McDowell ldquoIssues in Marketing and Brandingrdquo in Hand-book of Media Management and Economics A B Albarran SM Chan-Olmsted and M O Wirth Eds pp 229ndash250 LEANew Jersey NJ USA 2006

[9] E Katz and P F Lazarsfeld Personal Influence The Free PressNew York NY USA 1955

[10] R Ando and A Marinelli ldquoFare ricerca sul fandom on line Ifan italiani e le serie tvrdquo in Sociologia 20 Pratiche Sociali eMetodologie di Ricerca sui Media Partecipativi S Monaci andB Scifo Eds 2010 Scriptaweb httpscriptawebeuCatalogosociologia-2-0

[11] A de Kosnik ldquoShould fan fiction be freerdquo Cinema Journal vol48 no 4 pp 118ndash124 2009

[12] C Sandvoss Fans Polity Press Cambridge UK 2005[13] I Askwith TV 20 turning television into an engagement

medium [MS thesis] 2007 httpcmsmiteduresearchthesesIvanAskwith2007pdf

[14] P BoothDigital Fandom NewMedia Studies Peter Lung 2010[15] J Caldwell ldquoCritical industrial practice branding repurposing

and the migratory patterns of the industrial textsrdquo Television ampNew Media vol 7 pp 99ndash104 2006

[16] H Jenkins S Ford and J Green Spreadable Media NYU NewYork NY USA 2013

[17] E Benecchi and G Richeri ldquoTv to talk about engaging withAmerican tv series through the internetrdquo inThe New TelevisionEcosystem A Abbruzzese and L Fortunato Eds Peter LangBern Switzerland 2013

[18] J T Caldwell Production Culture Duke University PressDurham NC USA 2008

[19] H Jenkins Convergence Culture Where Old and New MediaCollide New York University Press New York NY USA 2006

Abstract and Applied Analysis 9

[20] M Hills Fan Cultures Routledge London UK 2003[21] N Baym Personal Connections in the Digital Age Polity Press

Cambridge UK 2000[22] I Condry ldquoCultures of music piracy an ethnographic com-

parison of the US and Japanrdquo International Journal of CulturalStudies vol 7 pp 343ndash363 2004

[23] AAustinH Jenkins J Green I Askwith and S Ford ldquoTurningpirates into loyalists the moral economy and an alternativeresponse to file sharingrdquo Tech Rep MIT Convergence CultureConsortium Cambridge UK 2006

[24] D Boyd Facebookrsquos Little Gifts Apophenia 2007[25] H Jenkins ldquoLook ListenWalk Technologyrdquo 2004 httpwww

technologyreviewcomInfoTechwtr 13560[26] M Scaglioni TV di culto La Serialita Televisiva Americana e il

Suo Fandom Vita e Pensiero Milano Italy 2006[27] L Porter and D Lavery ldquoCultivating a lost audience the part-

icipatory fan culture of lostrdquo in Unlocking the Meaning ofLost An Unauthorized Guide L Porter and D Lavery EdsSourcebooks Naperville Ill USA 2006

[28] C Hoskins and R Mirus ldquoReasons for the US dominanceof the international trade in television programmesrdquo MediaCulture and Society vol 10 pp 499ndash515 1988

[29] C Colapinto E Sartori andM Tolotti ldquoAwareness persuasionand adoption enriching the bassmodelrdquo Physica A vol 395 pp1ndash10 2014

[30] A Bucci C Colapinto M Forster and D la Torre ldquoStochastictechnology shocks in an extended Uzawa-Lucas model closed-form solution and long-run dynamicsrdquo Journal of EconomicsZeitschrift fur Nationalokonomie vol 103 no 1 pp 83ndash99 2011

[31] V Capasso R Engbers and D la Torre ldquoOn a spatial Solowmodel with technological diffusion and nonconcave productionfunctionrdquo Nonlinear Analysis Real World Applications vol 11no 5 pp 3858ndash3876 2010

[32] D la Torre and S Marsiglio ldquoEndogenous technologicalprogress in a multi-sector growth modelrdquo Economic Modellingvol 27 no 5 pp 1017ndash1028 2010

[33] D Bielby and C HarringtonGlobal TV NYU Press New YorkNY USA 2008

[34] C Tosenberger ldquoSaving people hunting thingsrdquo TransformativeWorks and Culture vol 4 2010

[35] H Jenkins ldquoSupernatural first impressionsrdquo Confessions of anACA-fan 2007 httphenryjenkinsorg200701supernaturalhtml

[36] L Zubernis and K Larsen Eds Fan Phenomena SupernaturalIntellect Books Bristol UK 2014

[37] M Wilson ldquoCW Exec Professes Support for Supernaturalrdquo2008 httpscifiaboutcomb20080122cw-exec-professes-support-for-supernaturalhtm

[38] T Goodman ldquoWomenrsquosMurder Club-bonding over crimerdquo SanFrancisco Chronicle October 2007

[39] A Stanley ldquoHomicide and Heelsrdquo The New York TimesOctober 2007

[40] Informa Telecoms and Media ldquoWorld most popular showsrdquoRadio Times August 2006

[41] ldquoAuditel datardquo httpwwwauditelit[42] H E Kunze D la Torre and E R Vrscay ldquoInverse problems

for random differential equations using the collage method forrandom contraction mappingsrdquo Journal of Computational andApplied Mathematics vol 223 no 2 pp 853ndash861 2009

[43] H Kunze D la Torre and E R Vrscay ldquoA generalized collagemethod based upon the Lax-Milgram functional for solvingboundary value inverse problemsrdquo Nonlinear Analysis TheoryMethods amp Applications vol 71 no 12 pp e1337ndashe1343 2009

[44] R Picard The Economics and Financing of Media CompaniesFordham University Press 2002

[45] M R Caputo Foundations of Dynamic Economic Analysis Opti-mal Control Theory and Applications Cambridge UniversityPress 2005

[46] T A Weber Optimal Control Theory with Applications inEconomics The MIT Press Cambridge Mass USA 2011

[47] H Jenkins Fans Bloggers and Gamers Media Consumer in theDigital Age Routledge London UK 2007

[48] E Benecchi andCColapinto ldquoEngagingwithGlee Transmediastorytelling for a television in transitionrdquo in Proceedings ofthe 25th International Conference of Communication (BusinessModels for a Digital Economy The Value of Contents) 2010

[49] J-C Rochet and J Tirole ldquoPlatform competition in two-sidedmarketsrdquo Journal of the European Economic Association vol 1no 4 pp 990ndash1029 2003

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Abstract and Applied Analysis 5

(b) If 120578 lt 120575 the product is not able to gain attentionand in the long run people will forget it

Women Murders Club a legal drama which ran on ABCfrom October 12 2007 to May 13 2008 was affected by the20072008 Writers Guild of America and by the subsequenterratic programming after the first 10 episodes were airedpeople had to wait 4 months to see the last 3 episodes theshow was also put in the Friday night prime time slot whichis considered a ldquodeath slotrdquo due to the concept that manyshows scheduled on or moved to Friday nights would not lastlong before cancellation due to low ratings From a receptionpoint of view not only the ratings were low (first seasonranked 57th with a medium of 8964m viewers) but alsothe critical response was tepid with Goodman [38] the SanFrancisco Chronicle TV critic publishing a highly criticalreview assigning the paperrsquos lowest possible rating and theNew York Times TV critic Stanley describing the show as ldquoallright but not good enoughrdquo [39] In fact Women MurdersClubwas cancelled onMay 12 2008 Mediaset had purchasedthe drama series before the strike judging just from the pilotand could not of course forecast the damages the strike wouldhave had on the development and even the ratings of manyAmerican TV showsWomenMurders Club suddenly becamean unwanted product because of the fast cancellation and thelack of popularity in the original country Mediaset ran theTV series first on the digital channel Joy part of its PremiumGallery and later because of the general lack of attentiondecides to use it to fill up the prime time slot of Canale5during the summer of 2010 The choice of programming anew drama series outside the guarantee period (11 Januaryndash30 June) is unusual but wise in this case the tepid receptionof the TV series first run both in US and in Italy the lack ofa previous successful campaign and of previous good resultsto build from and the small number of episodes availableconvinced the network that the series could not be consideredstrategic despite the fact that it was consistent to the channelidentity and target Women Murders Club is then offered tothe summer audience as a gift with a promotion built aroundits unusual scheduling (ldquoCanale5 offers you something neweven if it is Summerrdquo) and its resemblance to more populardramas (ldquoA mix between CSI Sex and The City and GreyrsquosAnatomyrdquo) The series is then used up as fast as possible inthe first week 4 episodes are aired in two nights (Tuesday andThursday) and from the second week the series is aired witha rhythm of 2 episodes per night on Thursday After a goodstart (1472 share and winner of the prime time) the ratingsdrop down week after week and the TV series is constantlysurpassed by old episodes of the scientific program Quarkaired by RAI in the same timeslot

(C) 120591 = 0 Under these hypotheses the solution is 119875(119905) =(119875(0)+120591(120578minus120575))119890

(120578minus120575)119905minus120591(120578minus120575) Different scenarios

can occur

(a) If 120578 gt 120575 then 119875 will increase providing asuccessful campaign whatever is the influencefrom abroad great investments in creating a

fandom would overturn the performance anddecrease the effects of bad reputation

The TV series Tequila and Bonetti (1992) inspired by themore popular movie Turner and Hooch (1989) starring TomHanks was aired by CBS from January 17th to April 18th1992 The detective comedy series was not a very successfulone and was cancelled after only 12 episodes Despite thatit proved to be a perfect match for the Italian channelItalia1 which aired the series repeatedly during the 1990sThe popularity of the TV series remained stable even aftermany years had passed since its last airing so much thatRete4 (Mediaset Group) started airing the TV series againin November 2009 What is even more interesting is thatafter 8 years from its cancellation in US a new season ofthe TV series was produced in Italy under the new title ofTequilaampBonetti (MastrofilmMediaTradeColumbia TriStarInternational Television 2000) Promotion and localizationof the series (Nick Bonetti was ldquotransferredrdquo in Rome andpartnered with an Italian celebrity in her first acting role)were independent from the American production and dis-tribution so much that the original producer Don Bellisarioonly discovered the existence of this second series years afterits first airing in Italy with obvious consequent legal issuesThe ldquolocalizedrdquo second season of the original American serieswas gifted with similar success and the 22 episodes airedrepeatedly on Italia1 and later on the satellite channels SkyShow (2008) and Sky Uno (2009) In this case the investmentin the promotion and adaptation of the TV series was hugedespite the lack of success of the product in the originalcountry of production

(b) If 120578 lt 120575 the popularity will tend to minus120591(120578minus120575) Inthis case the reputation and popularity abroadreally drive the internal performance

(b1) If 120591 is positive then the long run results ofthe campaign will end up in a success casewhose intensity is proportional to 120591

In this case the popularity of the TV series in the local marketis connected with the popularity of the TV series abroad CSIMiami (2002) the first spin-off of the forensic drama CSIarrived in Italy at the end of 2003 after the huge successregistered by the original CSI on the channel Italia1 and theevenmore huge success of the show in the worldwidemarketIt was not necessary to build up a big promotional campaignfor the TV series because the international success of the CSIfranchise was speaking for itself Later on CSI Miami waseven named the most popular program in the world becauseit featured in more countriesrsquo top 10 rankings for 2005 thanany other [40] and this data was used in the Italian promosfor the show Building from the international success of thefranchise and of the TV series itself CSI Miami soon becameone of themost viewed programs ofWednesday night and themost viewed series between the CSI franchises in Italy Theconfidence in the Italian success of CSI Miami is so strongthat in 2006 the series was even used to counterbalance theflop of the third season of The OC replacing the teen dramaon Sunday night and airing twice a week for months

6 Abstract and Applied Analysis

(b2) If 120591 is negative the fail in the foreign coun-tries will imply a decreasing popularity andeven worse the creation of people spreadingnegative comments on the product

This was the case of Defying Gravity a multinationallyproduced space travel drama which first aired on ABCin August 2009 The low ratings convinced the Americannetwork to suspend the series even if only 8 episodes outof the 13 produced had been aired When the debacle of theseries abroad was clear the Italian satellite channel Sky hadalready purchased the full first season and decided to air theproduct anyway on Fox Life starting 12 June 2010 in the lateprime time-slot (2155) The promotion and distribution ofthe show could not in this case profit from the internationalsuccess and had instead to fight against the bad popularity ofthe TV series which was even more evident because of thehigh profile promotion made in the original countryDefyingGravitywas in fact supposed to have 6 seasons 6 years was infact the length of the interplanetary voyage which plannedto visit most of the planets of the Solar System and wasmarketed as ldquoa Greyrsquos anatomy set in spacerdquo establishing adirect link with the most successful medical drama of ABCand playing with the fact that the two series had the sameproducing teamThis kind of promotionmade the seriesrsquo flopevenmore problematic for the international broadcasters Skyreused the ABC reference to Greyrsquos Anatomy a huge successin the Italianmarket too but tried to obscure any reference tosci-fi selling the show as a soap and adding to the main titlethe subtitle ldquothe galaxy of heartsrdquo The choice of schedulingDefying Gravity on Fox Lifemdashdedicated to family dramaand medicalsmdashand the late night summer slot-time thoughwere clear indications that the product was not consideredstrategic anymore because of the bad reputation it had gainedabroad

If 120578 = 0 then the popularity will tend to 120591120575 Thisis the case in Italy of the Law and Order franchise (1990)the success (120591 gt 0) of which is obviously disconnectedfrom the amount of local investments the dedication of thebroadcasting networks in the promotion and distributionarea for the single series in fact has always tended to zero inItaly This is shown by the small number of promos realizedfor each series all through their airing by the scheduling ofall the series in the late night or even in the night-time slotsand by the fact that they have been running both on RAIand Mediaset channels with no intention of connecting thesingle series to the specific channels Law and Order SVU forinstance has been used by Rete4 to fill up void spaces in thelate night schedule (between October and November 200710 out of the 22 episodes of the first season were aired inno particular order) before becoming the regular fill for thelate night time slot of the channel Law and Order timesloton Raidue often changed from daytime to late night andback again depending on the nature of the single episodewhile the 17th season (last one of the original series) has beenmoved to the prime time of Raitre Despite all the changes andlack of promotion the constant popularity of the TV seriesabroad and the strong niche following in Italy has made of

02468101214161820

0 20 40 60 80 100

times105

Figure 2 Popularity of Supernatural fades away

the Law and Order franchise a reliable show with specialregards to the ratings which remain constant

41 An Empirical Evidence As mention above in ItalySupernaturalrsquos performance has been affected by the lack of(or scarce) promotion and erratic scheduling (in particularshifting from springtime to summer a season characterizedby lower audience data)

Figure 2 shows the Auditel data [41] of the first four seriesof Supernatural broadcast on Rai2 channel in the period2007ndash2010 in detail the first season was broadcast duringFebruary-July 2007 the second June-September 2008 thethird July-September 2009 and the fourth July-August 2010The x axis shows the sequence of episodes whilst the y axislists the corresponding audience data

Figure 2 suggests that there are fluctuations of the dataaround the black trend line whose intensity is decreasingover time However Supernaturalrsquos long-run behavior can bewell approximated by the function 119875(119905) = 106119890minus0013119905 thatshows an exponential decay of popularity In particular thisempirical evidence shows that 120578 minus 120575 = minus0013 that is 120578 lt 120575implying that either 120578 = 0 (lack of promotion) or nonzero120578 lt 120575 (scarse promotion)

The parametric estimation has been done using thetechnique presented in [42 43] and based on the solution ofan inverse problem for a differential equation

5 An Optimal Decision ModelThe Decision Maker View Point

In a media company the decision maker faces the problemof maximizing profits subject to some constraints Mediacompanies must cover their costs (license fees productioncosts of programs ) and create returns just as any otherbusiness [44]The above formulatedmodel is purely dynamicand that does not provide any optimal decision rule Thepurpose of this section is indeed to formulate a dynamicprogramming model that can fully describe the complexityof a decision making process [45 46] We assume we havea closed market in which there is no influence of thepopularity of the product abroad and then 120591 is assumed to be

Abstract and Applied Analysis 7

zero With respect to the purely dynamic model previouslydescribed in which the term 120578 was supposed to be constantin this context we assume that 120578(119875(119905)) = Ω119875(119905) minus 120587(119905) whereΩ119875(119905) represents the revenues (depending on the level ofpopularity) that a TV company receives from the sale of adspaces to advertisers (Ω can be interpreted as the price of adspace) while 120587(119905) are the profits to be maximized by the DM

The difference Ω119875(119905) minus 120587(119905) is the investment in amarketing campaign The DM tries to maximize hisherintertemporal utility subject to a dynamic constraint thatdescribes the evolution of popularity and it can be formulatedas follows

Max int+infin

0

119880 (120587 (119905)) 119890

minus120588119905119889119905

st 119889119875 (119905)119889119905

= (minus120575 + Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

119875 (0) = 1198750

(3)

where 120588 is the discount rateThe variable 119875(119905) is the state variable while 120587(119905) is the

control For simplicity we assume a logarithmic utility119880 thatis 119880(120587(119905)) = ln(120587(119905)) even if other utility expressions couldbe considered analogously The following result states theexistence of a nontrivial equilibrium for the above dynamicmodel

Proposition 1 Suppose 120588 gt 120575 Then the above model showsthe existence of a nonzero equilibrium (119875lowast 120587lowast) where

119875

lowast=

120588

Ω

120587

lowast= 120588 minus 120575

(4)

Proof It is provided in the Appendix

In other words if the technical condition 120588 gt 120575 issatisfied this dynamic model shows the existence of a non-trivial equilibrium (119875lowast 120587lowast)The equilibrium of popularity119875lowastdepends on the price Ω and the higher will be the cost of amedia product for a customer the lower will be the level of119875lowastHowever as the analytical discussion in the Appendix showsthis equilibrium is unstable this practically means that onlyunder strict conditions the popularity will not vanish in thelong run

6 Conclusions

Internet provides tools that can alter the whole experienceof watching television giving access to the process not justthe results Through online communities in fact passionateviewers find and share a privileged knowledge which isderived both from the viewing experience and the extratex-tual elements of the show [21] According to recent studiesfans aremaking a new kind of television scene that transcendsplace and shakes up long-standing balances of power betweenfans and the television makers In general the most recentliterature published in the field of fan studies suggests that

the line between consumption and production is blurringinto a new paradigm with fans growing up to be creators andcreators trying to connect and engage with fan communitieswhen not labeling themselves as fans [13 21 47]

Themost successful TV series analyzed in this study havein fact been created promoted and distributed not onlytaking into account the existence of an active and internet-based fan audience but also relying on this same audience inorder to make the series an international success Comparedwith the ones that did not profit from the presence of afan audience or did not use connected marketing strategiesthese TV series have indeed succeeded in generating deepperpetual audience engagement

From a previous desk research and exploratory analysis[48] it emerged in fact that (a) there is a willingness toconsume texts offered by producers in different formatsoutside of the narrative space of the show itself and (b) partof the reason for this extratextual success lies in the initialconstruction and marketing of the show itself

Building from these results the model we propose heretries to identify and explain the main factors on whichthe popularity of American TV series in Italy is basedAll the examples confirm in fact the relevance of collateralactions specifically web orientated to underpin the successof televisionrsquos content as well as the influence of foreign popu-larity (globalization) which can be considered the explainingvariable involved in the success of a media product

The paper also introduces a decisional dynamic modelable to sustain the DM in hisher decisions In the Italianscenario commercial television plays a predominant role andcompetes to attract viewersrsquo attention and then sells thatattention to advertisers [49] In other words a broadcastingmedia platform can only succeed if it has viewers otherwiseits revenues from advertising would be zero As it is anadvertisement-supportedmedia from the two-sidedmarketsliterature we know that ad prices reflect both the value ofreaching a given audience and the marginal effect of theadvertisement sale on total audience size Thus popular TVprograms indirectly generate returns for a media companyattracting viewers Our model provides the DM the optimalsolution balancing the investment in sustaining programpopularity and the maximization of profits

For future works we aim at modifying this model byintroducing a stochastic term able to catch the naturalfluctuations arising from audience data

Appendix

In an optimal decision making process the DM tries to solvethe following model

Max int+infin

0

ln (120587 (119905)) 119890minus120588119905119889119905

st 119889119875 (119905)119889119905

= (minus120575 + Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

119875 (0) = 1198750

(5)

8 Abstract and Applied Analysis

The Hamiltonian associated with model (5) is

119867(119875 (119905) 120587 (119905)) = ln (120587 (119905)) 119890minus120588119905 + 120582 (119905)

times (minus120575119875 (119905) + (Ω119875 (119905) minus 120587 (119905)) 119875 (119905))

(6)

Optimality conditions for (6) read as

0 =

120597119867

120597120587

=

119890

minus120588119905

120587 (119905)

minus 120582 (119905) 119875 (119905)

minus

120582 (119905) =

120597119867

120597119875

= 120582 (119905) (minus120575 + 2Ω119875 (119905) minus 120587 (119905))

119875 (119905) =

120597119867

120597120582

= minus120575119875 (119905) + (Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

(7)

The system (7) is equivalent to

120587 (119905) =

119890

minus120588119905

120582 (119905) 119875 (119905)

997904rArr

(119905)

120587 (119905)

= minus120588 minus

120582 (119905)

120582 (119905)

minus

119875 (119905)

119875 (119905)

minus

120582 (119905) = 120582 (119905) (minus120575 + 2Ω119875 (119905) minus 120587 (119905))

997904rArr minus

120582 (119905)

120582 (119905)

= minus120575 + 2Ω119875 (119905) minus 120587 (119905)

119875 (119905) = minus120575119875 (119905) + (Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

997904rArr

119875 (119905)

119875 (119905)

= minus120575 + Ω119875 (119905) minus 120587 (119905)

(8)

which implies

(119905)

120587 (119905)

= minus120588 + Ω119875 (119905)

119875 (119905)

119875 (119905)

= minus120575 + Ω119875 (119905) minus 120587 (119905)

(9)

The only nontrivial equilibrium is

119875

lowast=

120588

Ω

120587

lowast= 120588 minus 120575 gt 0

(10)

The Jacobian of the linearized system at (119875lowast 120587lowast) is equal to

119869 = [

0 Ω (120588 minus 120575)

minus

120588

Ω

120588

] (11)

The determinant of 119869 is equal to

det (119869) = 120588 (120588 minus 120575) gt 0 (12)

while the trace of 119869 is equal to

trace (119869) = 120588 gt 0 (13)

which implies that (119875lowast 120587lowast) is an unstable equilibrium Itis possible to show that this system admits three moreequilibria namely (0 0) (119875lowast 0) and (0 120587lowast) Among them(0 0) and (0 120587lowast) are locally asymptotically stable

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] C Colapinto ldquoMoving to a multichannel and multiplatformcompany in the emerging and digital media ecosystem the caseof mediaset grouprdquo International Journal on Media Manage-ment vol 12 no 2 pp 59ndash75 2010

[2] TWeinbergTheNewCommunity RulesMarketing on the SocialWeb OrsquoReilly Media Inc Sebastopol Calif USA 2009

[3] C Colapinto and E Benecchi ldquoMovie industry goes viral inthe XXIst century if what counts is the buzzrdquo in CrossmediaInnovations I Ibrus and C A Scolari Eds pp 161ndash178 PeterLang Berlin Germany 2012

[4] C Colapinto and E Benecchi ldquoThe presentation of celebritypersonas in everyday twittering managing online reputationsthroughout a communication crisisrdquo Media Culture amp Societyvol 36 pp 219ndash233 2014

[5] A Toffler Future Shock William Morrow and Company NewYork NY USA 1980

[6] L Kung Strategic Management in the Media SAGE LondonUK 2008

[7] M PMcAllister and J Turrow ldquoNewmedia and the commercialsphere two intersecting trends five categories of concernrdquoJournal of Broadcasting amp Electronic Media vol 46 no 4 pp505ndash514 2002

[8] W S McDowell ldquoIssues in Marketing and Brandingrdquo in Hand-book of Media Management and Economics A B Albarran SM Chan-Olmsted and M O Wirth Eds pp 229ndash250 LEANew Jersey NJ USA 2006

[9] E Katz and P F Lazarsfeld Personal Influence The Free PressNew York NY USA 1955

[10] R Ando and A Marinelli ldquoFare ricerca sul fandom on line Ifan italiani e le serie tvrdquo in Sociologia 20 Pratiche Sociali eMetodologie di Ricerca sui Media Partecipativi S Monaci andB Scifo Eds 2010 Scriptaweb httpscriptawebeuCatalogosociologia-2-0

[11] A de Kosnik ldquoShould fan fiction be freerdquo Cinema Journal vol48 no 4 pp 118ndash124 2009

[12] C Sandvoss Fans Polity Press Cambridge UK 2005[13] I Askwith TV 20 turning television into an engagement

medium [MS thesis] 2007 httpcmsmiteduresearchthesesIvanAskwith2007pdf

[14] P BoothDigital Fandom NewMedia Studies Peter Lung 2010[15] J Caldwell ldquoCritical industrial practice branding repurposing

and the migratory patterns of the industrial textsrdquo Television ampNew Media vol 7 pp 99ndash104 2006

[16] H Jenkins S Ford and J Green Spreadable Media NYU NewYork NY USA 2013

[17] E Benecchi and G Richeri ldquoTv to talk about engaging withAmerican tv series through the internetrdquo inThe New TelevisionEcosystem A Abbruzzese and L Fortunato Eds Peter LangBern Switzerland 2013

[18] J T Caldwell Production Culture Duke University PressDurham NC USA 2008

[19] H Jenkins Convergence Culture Where Old and New MediaCollide New York University Press New York NY USA 2006

Abstract and Applied Analysis 9

[20] M Hills Fan Cultures Routledge London UK 2003[21] N Baym Personal Connections in the Digital Age Polity Press

Cambridge UK 2000[22] I Condry ldquoCultures of music piracy an ethnographic com-

parison of the US and Japanrdquo International Journal of CulturalStudies vol 7 pp 343ndash363 2004

[23] AAustinH Jenkins J Green I Askwith and S Ford ldquoTurningpirates into loyalists the moral economy and an alternativeresponse to file sharingrdquo Tech Rep MIT Convergence CultureConsortium Cambridge UK 2006

[24] D Boyd Facebookrsquos Little Gifts Apophenia 2007[25] H Jenkins ldquoLook ListenWalk Technologyrdquo 2004 httpwww

technologyreviewcomInfoTechwtr 13560[26] M Scaglioni TV di culto La Serialita Televisiva Americana e il

Suo Fandom Vita e Pensiero Milano Italy 2006[27] L Porter and D Lavery ldquoCultivating a lost audience the part-

icipatory fan culture of lostrdquo in Unlocking the Meaning ofLost An Unauthorized Guide L Porter and D Lavery EdsSourcebooks Naperville Ill USA 2006

[28] C Hoskins and R Mirus ldquoReasons for the US dominanceof the international trade in television programmesrdquo MediaCulture and Society vol 10 pp 499ndash515 1988

[29] C Colapinto E Sartori andM Tolotti ldquoAwareness persuasionand adoption enriching the bassmodelrdquo Physica A vol 395 pp1ndash10 2014

[30] A Bucci C Colapinto M Forster and D la Torre ldquoStochastictechnology shocks in an extended Uzawa-Lucas model closed-form solution and long-run dynamicsrdquo Journal of EconomicsZeitschrift fur Nationalokonomie vol 103 no 1 pp 83ndash99 2011

[31] V Capasso R Engbers and D la Torre ldquoOn a spatial Solowmodel with technological diffusion and nonconcave productionfunctionrdquo Nonlinear Analysis Real World Applications vol 11no 5 pp 3858ndash3876 2010

[32] D la Torre and S Marsiglio ldquoEndogenous technologicalprogress in a multi-sector growth modelrdquo Economic Modellingvol 27 no 5 pp 1017ndash1028 2010

[33] D Bielby and C HarringtonGlobal TV NYU Press New YorkNY USA 2008

[34] C Tosenberger ldquoSaving people hunting thingsrdquo TransformativeWorks and Culture vol 4 2010

[35] H Jenkins ldquoSupernatural first impressionsrdquo Confessions of anACA-fan 2007 httphenryjenkinsorg200701supernaturalhtml

[36] L Zubernis and K Larsen Eds Fan Phenomena SupernaturalIntellect Books Bristol UK 2014

[37] M Wilson ldquoCW Exec Professes Support for Supernaturalrdquo2008 httpscifiaboutcomb20080122cw-exec-professes-support-for-supernaturalhtm

[38] T Goodman ldquoWomenrsquosMurder Club-bonding over crimerdquo SanFrancisco Chronicle October 2007

[39] A Stanley ldquoHomicide and Heelsrdquo The New York TimesOctober 2007

[40] Informa Telecoms and Media ldquoWorld most popular showsrdquoRadio Times August 2006

[41] ldquoAuditel datardquo httpwwwauditelit[42] H E Kunze D la Torre and E R Vrscay ldquoInverse problems

for random differential equations using the collage method forrandom contraction mappingsrdquo Journal of Computational andApplied Mathematics vol 223 no 2 pp 853ndash861 2009

[43] H Kunze D la Torre and E R Vrscay ldquoA generalized collagemethod based upon the Lax-Milgram functional for solvingboundary value inverse problemsrdquo Nonlinear Analysis TheoryMethods amp Applications vol 71 no 12 pp e1337ndashe1343 2009

[44] R Picard The Economics and Financing of Media CompaniesFordham University Press 2002

[45] M R Caputo Foundations of Dynamic Economic Analysis Opti-mal Control Theory and Applications Cambridge UniversityPress 2005

[46] T A Weber Optimal Control Theory with Applications inEconomics The MIT Press Cambridge Mass USA 2011

[47] H Jenkins Fans Bloggers and Gamers Media Consumer in theDigital Age Routledge London UK 2007

[48] E Benecchi andCColapinto ldquoEngagingwithGlee Transmediastorytelling for a television in transitionrdquo in Proceedings ofthe 25th International Conference of Communication (BusinessModels for a Digital Economy The Value of Contents) 2010

[49] J-C Rochet and J Tirole ldquoPlatform competition in two-sidedmarketsrdquo Journal of the European Economic Association vol 1no 4 pp 990ndash1029 2003

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

6 Abstract and Applied Analysis

(b2) If 120591 is negative the fail in the foreign coun-tries will imply a decreasing popularity andeven worse the creation of people spreadingnegative comments on the product

This was the case of Defying Gravity a multinationallyproduced space travel drama which first aired on ABCin August 2009 The low ratings convinced the Americannetwork to suspend the series even if only 8 episodes outof the 13 produced had been aired When the debacle of theseries abroad was clear the Italian satellite channel Sky hadalready purchased the full first season and decided to air theproduct anyway on Fox Life starting 12 June 2010 in the lateprime time-slot (2155) The promotion and distribution ofthe show could not in this case profit from the internationalsuccess and had instead to fight against the bad popularity ofthe TV series which was even more evident because of thehigh profile promotion made in the original countryDefyingGravitywas in fact supposed to have 6 seasons 6 years was infact the length of the interplanetary voyage which plannedto visit most of the planets of the Solar System and wasmarketed as ldquoa Greyrsquos anatomy set in spacerdquo establishing adirect link with the most successful medical drama of ABCand playing with the fact that the two series had the sameproducing teamThis kind of promotionmade the seriesrsquo flopevenmore problematic for the international broadcasters Skyreused the ABC reference to Greyrsquos Anatomy a huge successin the Italianmarket too but tried to obscure any reference tosci-fi selling the show as a soap and adding to the main titlethe subtitle ldquothe galaxy of heartsrdquo The choice of schedulingDefying Gravity on Fox Lifemdashdedicated to family dramaand medicalsmdashand the late night summer slot-time thoughwere clear indications that the product was not consideredstrategic anymore because of the bad reputation it had gainedabroad

If 120578 = 0 then the popularity will tend to 120591120575 Thisis the case in Italy of the Law and Order franchise (1990)the success (120591 gt 0) of which is obviously disconnectedfrom the amount of local investments the dedication of thebroadcasting networks in the promotion and distributionarea for the single series in fact has always tended to zero inItaly This is shown by the small number of promos realizedfor each series all through their airing by the scheduling ofall the series in the late night or even in the night-time slotsand by the fact that they have been running both on RAIand Mediaset channels with no intention of connecting thesingle series to the specific channels Law and Order SVU forinstance has been used by Rete4 to fill up void spaces in thelate night schedule (between October and November 200710 out of the 22 episodes of the first season were aired inno particular order) before becoming the regular fill for thelate night time slot of the channel Law and Order timesloton Raidue often changed from daytime to late night andback again depending on the nature of the single episodewhile the 17th season (last one of the original series) has beenmoved to the prime time of Raitre Despite all the changes andlack of promotion the constant popularity of the TV seriesabroad and the strong niche following in Italy has made of

02468101214161820

0 20 40 60 80 100

times105

Figure 2 Popularity of Supernatural fades away

the Law and Order franchise a reliable show with specialregards to the ratings which remain constant

41 An Empirical Evidence As mention above in ItalySupernaturalrsquos performance has been affected by the lack of(or scarce) promotion and erratic scheduling (in particularshifting from springtime to summer a season characterizedby lower audience data)

Figure 2 shows the Auditel data [41] of the first four seriesof Supernatural broadcast on Rai2 channel in the period2007ndash2010 in detail the first season was broadcast duringFebruary-July 2007 the second June-September 2008 thethird July-September 2009 and the fourth July-August 2010The x axis shows the sequence of episodes whilst the y axislists the corresponding audience data

Figure 2 suggests that there are fluctuations of the dataaround the black trend line whose intensity is decreasingover time However Supernaturalrsquos long-run behavior can bewell approximated by the function 119875(119905) = 106119890minus0013119905 thatshows an exponential decay of popularity In particular thisempirical evidence shows that 120578 minus 120575 = minus0013 that is 120578 lt 120575implying that either 120578 = 0 (lack of promotion) or nonzero120578 lt 120575 (scarse promotion)

The parametric estimation has been done using thetechnique presented in [42 43] and based on the solution ofan inverse problem for a differential equation

5 An Optimal Decision ModelThe Decision Maker View Point

In a media company the decision maker faces the problemof maximizing profits subject to some constraints Mediacompanies must cover their costs (license fees productioncosts of programs ) and create returns just as any otherbusiness [44]The above formulatedmodel is purely dynamicand that does not provide any optimal decision rule Thepurpose of this section is indeed to formulate a dynamicprogramming model that can fully describe the complexityof a decision making process [45 46] We assume we havea closed market in which there is no influence of thepopularity of the product abroad and then 120591 is assumed to be

Abstract and Applied Analysis 7

zero With respect to the purely dynamic model previouslydescribed in which the term 120578 was supposed to be constantin this context we assume that 120578(119875(119905)) = Ω119875(119905) minus 120587(119905) whereΩ119875(119905) represents the revenues (depending on the level ofpopularity) that a TV company receives from the sale of adspaces to advertisers (Ω can be interpreted as the price of adspace) while 120587(119905) are the profits to be maximized by the DM

The difference Ω119875(119905) minus 120587(119905) is the investment in amarketing campaign The DM tries to maximize hisherintertemporal utility subject to a dynamic constraint thatdescribes the evolution of popularity and it can be formulatedas follows

Max int+infin

0

119880 (120587 (119905)) 119890

minus120588119905119889119905

st 119889119875 (119905)119889119905

= (minus120575 + Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

119875 (0) = 1198750

(3)

where 120588 is the discount rateThe variable 119875(119905) is the state variable while 120587(119905) is the

control For simplicity we assume a logarithmic utility119880 thatis 119880(120587(119905)) = ln(120587(119905)) even if other utility expressions couldbe considered analogously The following result states theexistence of a nontrivial equilibrium for the above dynamicmodel

Proposition 1 Suppose 120588 gt 120575 Then the above model showsthe existence of a nonzero equilibrium (119875lowast 120587lowast) where

119875

lowast=

120588

Ω

120587

lowast= 120588 minus 120575

(4)

Proof It is provided in the Appendix

In other words if the technical condition 120588 gt 120575 issatisfied this dynamic model shows the existence of a non-trivial equilibrium (119875lowast 120587lowast)The equilibrium of popularity119875lowastdepends on the price Ω and the higher will be the cost of amedia product for a customer the lower will be the level of119875lowastHowever as the analytical discussion in the Appendix showsthis equilibrium is unstable this practically means that onlyunder strict conditions the popularity will not vanish in thelong run

6 Conclusions

Internet provides tools that can alter the whole experienceof watching television giving access to the process not justthe results Through online communities in fact passionateviewers find and share a privileged knowledge which isderived both from the viewing experience and the extratex-tual elements of the show [21] According to recent studiesfans aremaking a new kind of television scene that transcendsplace and shakes up long-standing balances of power betweenfans and the television makers In general the most recentliterature published in the field of fan studies suggests that

the line between consumption and production is blurringinto a new paradigm with fans growing up to be creators andcreators trying to connect and engage with fan communitieswhen not labeling themselves as fans [13 21 47]

Themost successful TV series analyzed in this study havein fact been created promoted and distributed not onlytaking into account the existence of an active and internet-based fan audience but also relying on this same audience inorder to make the series an international success Comparedwith the ones that did not profit from the presence of afan audience or did not use connected marketing strategiesthese TV series have indeed succeeded in generating deepperpetual audience engagement

From a previous desk research and exploratory analysis[48] it emerged in fact that (a) there is a willingness toconsume texts offered by producers in different formatsoutside of the narrative space of the show itself and (b) partof the reason for this extratextual success lies in the initialconstruction and marketing of the show itself

Building from these results the model we propose heretries to identify and explain the main factors on whichthe popularity of American TV series in Italy is basedAll the examples confirm in fact the relevance of collateralactions specifically web orientated to underpin the successof televisionrsquos content as well as the influence of foreign popu-larity (globalization) which can be considered the explainingvariable involved in the success of a media product

The paper also introduces a decisional dynamic modelable to sustain the DM in hisher decisions In the Italianscenario commercial television plays a predominant role andcompetes to attract viewersrsquo attention and then sells thatattention to advertisers [49] In other words a broadcastingmedia platform can only succeed if it has viewers otherwiseits revenues from advertising would be zero As it is anadvertisement-supportedmedia from the two-sidedmarketsliterature we know that ad prices reflect both the value ofreaching a given audience and the marginal effect of theadvertisement sale on total audience size Thus popular TVprograms indirectly generate returns for a media companyattracting viewers Our model provides the DM the optimalsolution balancing the investment in sustaining programpopularity and the maximization of profits

For future works we aim at modifying this model byintroducing a stochastic term able to catch the naturalfluctuations arising from audience data

Appendix

In an optimal decision making process the DM tries to solvethe following model

Max int+infin

0

ln (120587 (119905)) 119890minus120588119905119889119905

st 119889119875 (119905)119889119905

= (minus120575 + Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

119875 (0) = 1198750

(5)

8 Abstract and Applied Analysis

The Hamiltonian associated with model (5) is

119867(119875 (119905) 120587 (119905)) = ln (120587 (119905)) 119890minus120588119905 + 120582 (119905)

times (minus120575119875 (119905) + (Ω119875 (119905) minus 120587 (119905)) 119875 (119905))

(6)

Optimality conditions for (6) read as

0 =

120597119867

120597120587

=

119890

minus120588119905

120587 (119905)

minus 120582 (119905) 119875 (119905)

minus

120582 (119905) =

120597119867

120597119875

= 120582 (119905) (minus120575 + 2Ω119875 (119905) minus 120587 (119905))

119875 (119905) =

120597119867

120597120582

= minus120575119875 (119905) + (Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

(7)

The system (7) is equivalent to

120587 (119905) =

119890

minus120588119905

120582 (119905) 119875 (119905)

997904rArr

(119905)

120587 (119905)

= minus120588 minus

120582 (119905)

120582 (119905)

minus

119875 (119905)

119875 (119905)

minus

120582 (119905) = 120582 (119905) (minus120575 + 2Ω119875 (119905) minus 120587 (119905))

997904rArr minus

120582 (119905)

120582 (119905)

= minus120575 + 2Ω119875 (119905) minus 120587 (119905)

119875 (119905) = minus120575119875 (119905) + (Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

997904rArr

119875 (119905)

119875 (119905)

= minus120575 + Ω119875 (119905) minus 120587 (119905)

(8)

which implies

(119905)

120587 (119905)

= minus120588 + Ω119875 (119905)

119875 (119905)

119875 (119905)

= minus120575 + Ω119875 (119905) minus 120587 (119905)

(9)

The only nontrivial equilibrium is

119875

lowast=

120588

Ω

120587

lowast= 120588 minus 120575 gt 0

(10)

The Jacobian of the linearized system at (119875lowast 120587lowast) is equal to

119869 = [

0 Ω (120588 minus 120575)

minus

120588

Ω

120588

] (11)

The determinant of 119869 is equal to

det (119869) = 120588 (120588 minus 120575) gt 0 (12)

while the trace of 119869 is equal to

trace (119869) = 120588 gt 0 (13)

which implies that (119875lowast 120587lowast) is an unstable equilibrium Itis possible to show that this system admits three moreequilibria namely (0 0) (119875lowast 0) and (0 120587lowast) Among them(0 0) and (0 120587lowast) are locally asymptotically stable

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] C Colapinto ldquoMoving to a multichannel and multiplatformcompany in the emerging and digital media ecosystem the caseof mediaset grouprdquo International Journal on Media Manage-ment vol 12 no 2 pp 59ndash75 2010

[2] TWeinbergTheNewCommunity RulesMarketing on the SocialWeb OrsquoReilly Media Inc Sebastopol Calif USA 2009

[3] C Colapinto and E Benecchi ldquoMovie industry goes viral inthe XXIst century if what counts is the buzzrdquo in CrossmediaInnovations I Ibrus and C A Scolari Eds pp 161ndash178 PeterLang Berlin Germany 2012

[4] C Colapinto and E Benecchi ldquoThe presentation of celebritypersonas in everyday twittering managing online reputationsthroughout a communication crisisrdquo Media Culture amp Societyvol 36 pp 219ndash233 2014

[5] A Toffler Future Shock William Morrow and Company NewYork NY USA 1980

[6] L Kung Strategic Management in the Media SAGE LondonUK 2008

[7] M PMcAllister and J Turrow ldquoNewmedia and the commercialsphere two intersecting trends five categories of concernrdquoJournal of Broadcasting amp Electronic Media vol 46 no 4 pp505ndash514 2002

[8] W S McDowell ldquoIssues in Marketing and Brandingrdquo in Hand-book of Media Management and Economics A B Albarran SM Chan-Olmsted and M O Wirth Eds pp 229ndash250 LEANew Jersey NJ USA 2006

[9] E Katz and P F Lazarsfeld Personal Influence The Free PressNew York NY USA 1955

[10] R Ando and A Marinelli ldquoFare ricerca sul fandom on line Ifan italiani e le serie tvrdquo in Sociologia 20 Pratiche Sociali eMetodologie di Ricerca sui Media Partecipativi S Monaci andB Scifo Eds 2010 Scriptaweb httpscriptawebeuCatalogosociologia-2-0

[11] A de Kosnik ldquoShould fan fiction be freerdquo Cinema Journal vol48 no 4 pp 118ndash124 2009

[12] C Sandvoss Fans Polity Press Cambridge UK 2005[13] I Askwith TV 20 turning television into an engagement

medium [MS thesis] 2007 httpcmsmiteduresearchthesesIvanAskwith2007pdf

[14] P BoothDigital Fandom NewMedia Studies Peter Lung 2010[15] J Caldwell ldquoCritical industrial practice branding repurposing

and the migratory patterns of the industrial textsrdquo Television ampNew Media vol 7 pp 99ndash104 2006

[16] H Jenkins S Ford and J Green Spreadable Media NYU NewYork NY USA 2013

[17] E Benecchi and G Richeri ldquoTv to talk about engaging withAmerican tv series through the internetrdquo inThe New TelevisionEcosystem A Abbruzzese and L Fortunato Eds Peter LangBern Switzerland 2013

[18] J T Caldwell Production Culture Duke University PressDurham NC USA 2008

[19] H Jenkins Convergence Culture Where Old and New MediaCollide New York University Press New York NY USA 2006

Abstract and Applied Analysis 9

[20] M Hills Fan Cultures Routledge London UK 2003[21] N Baym Personal Connections in the Digital Age Polity Press

Cambridge UK 2000[22] I Condry ldquoCultures of music piracy an ethnographic com-

parison of the US and Japanrdquo International Journal of CulturalStudies vol 7 pp 343ndash363 2004

[23] AAustinH Jenkins J Green I Askwith and S Ford ldquoTurningpirates into loyalists the moral economy and an alternativeresponse to file sharingrdquo Tech Rep MIT Convergence CultureConsortium Cambridge UK 2006

[24] D Boyd Facebookrsquos Little Gifts Apophenia 2007[25] H Jenkins ldquoLook ListenWalk Technologyrdquo 2004 httpwww

technologyreviewcomInfoTechwtr 13560[26] M Scaglioni TV di culto La Serialita Televisiva Americana e il

Suo Fandom Vita e Pensiero Milano Italy 2006[27] L Porter and D Lavery ldquoCultivating a lost audience the part-

icipatory fan culture of lostrdquo in Unlocking the Meaning ofLost An Unauthorized Guide L Porter and D Lavery EdsSourcebooks Naperville Ill USA 2006

[28] C Hoskins and R Mirus ldquoReasons for the US dominanceof the international trade in television programmesrdquo MediaCulture and Society vol 10 pp 499ndash515 1988

[29] C Colapinto E Sartori andM Tolotti ldquoAwareness persuasionand adoption enriching the bassmodelrdquo Physica A vol 395 pp1ndash10 2014

[30] A Bucci C Colapinto M Forster and D la Torre ldquoStochastictechnology shocks in an extended Uzawa-Lucas model closed-form solution and long-run dynamicsrdquo Journal of EconomicsZeitschrift fur Nationalokonomie vol 103 no 1 pp 83ndash99 2011

[31] V Capasso R Engbers and D la Torre ldquoOn a spatial Solowmodel with technological diffusion and nonconcave productionfunctionrdquo Nonlinear Analysis Real World Applications vol 11no 5 pp 3858ndash3876 2010

[32] D la Torre and S Marsiglio ldquoEndogenous technologicalprogress in a multi-sector growth modelrdquo Economic Modellingvol 27 no 5 pp 1017ndash1028 2010

[33] D Bielby and C HarringtonGlobal TV NYU Press New YorkNY USA 2008

[34] C Tosenberger ldquoSaving people hunting thingsrdquo TransformativeWorks and Culture vol 4 2010

[35] H Jenkins ldquoSupernatural first impressionsrdquo Confessions of anACA-fan 2007 httphenryjenkinsorg200701supernaturalhtml

[36] L Zubernis and K Larsen Eds Fan Phenomena SupernaturalIntellect Books Bristol UK 2014

[37] M Wilson ldquoCW Exec Professes Support for Supernaturalrdquo2008 httpscifiaboutcomb20080122cw-exec-professes-support-for-supernaturalhtm

[38] T Goodman ldquoWomenrsquosMurder Club-bonding over crimerdquo SanFrancisco Chronicle October 2007

[39] A Stanley ldquoHomicide and Heelsrdquo The New York TimesOctober 2007

[40] Informa Telecoms and Media ldquoWorld most popular showsrdquoRadio Times August 2006

[41] ldquoAuditel datardquo httpwwwauditelit[42] H E Kunze D la Torre and E R Vrscay ldquoInverse problems

for random differential equations using the collage method forrandom contraction mappingsrdquo Journal of Computational andApplied Mathematics vol 223 no 2 pp 853ndash861 2009

[43] H Kunze D la Torre and E R Vrscay ldquoA generalized collagemethod based upon the Lax-Milgram functional for solvingboundary value inverse problemsrdquo Nonlinear Analysis TheoryMethods amp Applications vol 71 no 12 pp e1337ndashe1343 2009

[44] R Picard The Economics and Financing of Media CompaniesFordham University Press 2002

[45] M R Caputo Foundations of Dynamic Economic Analysis Opti-mal Control Theory and Applications Cambridge UniversityPress 2005

[46] T A Weber Optimal Control Theory with Applications inEconomics The MIT Press Cambridge Mass USA 2011

[47] H Jenkins Fans Bloggers and Gamers Media Consumer in theDigital Age Routledge London UK 2007

[48] E Benecchi andCColapinto ldquoEngagingwithGlee Transmediastorytelling for a television in transitionrdquo in Proceedings ofthe 25th International Conference of Communication (BusinessModels for a Digital Economy The Value of Contents) 2010

[49] J-C Rochet and J Tirole ldquoPlatform competition in two-sidedmarketsrdquo Journal of the European Economic Association vol 1no 4 pp 990ndash1029 2003

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Abstract and Applied Analysis 7

zero With respect to the purely dynamic model previouslydescribed in which the term 120578 was supposed to be constantin this context we assume that 120578(119875(119905)) = Ω119875(119905) minus 120587(119905) whereΩ119875(119905) represents the revenues (depending on the level ofpopularity) that a TV company receives from the sale of adspaces to advertisers (Ω can be interpreted as the price of adspace) while 120587(119905) are the profits to be maximized by the DM

The difference Ω119875(119905) minus 120587(119905) is the investment in amarketing campaign The DM tries to maximize hisherintertemporal utility subject to a dynamic constraint thatdescribes the evolution of popularity and it can be formulatedas follows

Max int+infin

0

119880 (120587 (119905)) 119890

minus120588119905119889119905

st 119889119875 (119905)119889119905

= (minus120575 + Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

119875 (0) = 1198750

(3)

where 120588 is the discount rateThe variable 119875(119905) is the state variable while 120587(119905) is the

control For simplicity we assume a logarithmic utility119880 thatis 119880(120587(119905)) = ln(120587(119905)) even if other utility expressions couldbe considered analogously The following result states theexistence of a nontrivial equilibrium for the above dynamicmodel

Proposition 1 Suppose 120588 gt 120575 Then the above model showsthe existence of a nonzero equilibrium (119875lowast 120587lowast) where

119875

lowast=

120588

Ω

120587

lowast= 120588 minus 120575

(4)

Proof It is provided in the Appendix

In other words if the technical condition 120588 gt 120575 issatisfied this dynamic model shows the existence of a non-trivial equilibrium (119875lowast 120587lowast)The equilibrium of popularity119875lowastdepends on the price Ω and the higher will be the cost of amedia product for a customer the lower will be the level of119875lowastHowever as the analytical discussion in the Appendix showsthis equilibrium is unstable this practically means that onlyunder strict conditions the popularity will not vanish in thelong run

6 Conclusions

Internet provides tools that can alter the whole experienceof watching television giving access to the process not justthe results Through online communities in fact passionateviewers find and share a privileged knowledge which isderived both from the viewing experience and the extratex-tual elements of the show [21] According to recent studiesfans aremaking a new kind of television scene that transcendsplace and shakes up long-standing balances of power betweenfans and the television makers In general the most recentliterature published in the field of fan studies suggests that

the line between consumption and production is blurringinto a new paradigm with fans growing up to be creators andcreators trying to connect and engage with fan communitieswhen not labeling themselves as fans [13 21 47]

Themost successful TV series analyzed in this study havein fact been created promoted and distributed not onlytaking into account the existence of an active and internet-based fan audience but also relying on this same audience inorder to make the series an international success Comparedwith the ones that did not profit from the presence of afan audience or did not use connected marketing strategiesthese TV series have indeed succeeded in generating deepperpetual audience engagement

From a previous desk research and exploratory analysis[48] it emerged in fact that (a) there is a willingness toconsume texts offered by producers in different formatsoutside of the narrative space of the show itself and (b) partof the reason for this extratextual success lies in the initialconstruction and marketing of the show itself

Building from these results the model we propose heretries to identify and explain the main factors on whichthe popularity of American TV series in Italy is basedAll the examples confirm in fact the relevance of collateralactions specifically web orientated to underpin the successof televisionrsquos content as well as the influence of foreign popu-larity (globalization) which can be considered the explainingvariable involved in the success of a media product

The paper also introduces a decisional dynamic modelable to sustain the DM in hisher decisions In the Italianscenario commercial television plays a predominant role andcompetes to attract viewersrsquo attention and then sells thatattention to advertisers [49] In other words a broadcastingmedia platform can only succeed if it has viewers otherwiseits revenues from advertising would be zero As it is anadvertisement-supportedmedia from the two-sidedmarketsliterature we know that ad prices reflect both the value ofreaching a given audience and the marginal effect of theadvertisement sale on total audience size Thus popular TVprograms indirectly generate returns for a media companyattracting viewers Our model provides the DM the optimalsolution balancing the investment in sustaining programpopularity and the maximization of profits

For future works we aim at modifying this model byintroducing a stochastic term able to catch the naturalfluctuations arising from audience data

Appendix

In an optimal decision making process the DM tries to solvethe following model

Max int+infin

0

ln (120587 (119905)) 119890minus120588119905119889119905

st 119889119875 (119905)119889119905

= (minus120575 + Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

119875 (0) = 1198750

(5)

8 Abstract and Applied Analysis

The Hamiltonian associated with model (5) is

119867(119875 (119905) 120587 (119905)) = ln (120587 (119905)) 119890minus120588119905 + 120582 (119905)

times (minus120575119875 (119905) + (Ω119875 (119905) minus 120587 (119905)) 119875 (119905))

(6)

Optimality conditions for (6) read as

0 =

120597119867

120597120587

=

119890

minus120588119905

120587 (119905)

minus 120582 (119905) 119875 (119905)

minus

120582 (119905) =

120597119867

120597119875

= 120582 (119905) (minus120575 + 2Ω119875 (119905) minus 120587 (119905))

119875 (119905) =

120597119867

120597120582

= minus120575119875 (119905) + (Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

(7)

The system (7) is equivalent to

120587 (119905) =

119890

minus120588119905

120582 (119905) 119875 (119905)

997904rArr

(119905)

120587 (119905)

= minus120588 minus

120582 (119905)

120582 (119905)

minus

119875 (119905)

119875 (119905)

minus

120582 (119905) = 120582 (119905) (minus120575 + 2Ω119875 (119905) minus 120587 (119905))

997904rArr minus

120582 (119905)

120582 (119905)

= minus120575 + 2Ω119875 (119905) minus 120587 (119905)

119875 (119905) = minus120575119875 (119905) + (Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

997904rArr

119875 (119905)

119875 (119905)

= minus120575 + Ω119875 (119905) minus 120587 (119905)

(8)

which implies

(119905)

120587 (119905)

= minus120588 + Ω119875 (119905)

119875 (119905)

119875 (119905)

= minus120575 + Ω119875 (119905) minus 120587 (119905)

(9)

The only nontrivial equilibrium is

119875

lowast=

120588

Ω

120587

lowast= 120588 minus 120575 gt 0

(10)

The Jacobian of the linearized system at (119875lowast 120587lowast) is equal to

119869 = [

0 Ω (120588 minus 120575)

minus

120588

Ω

120588

] (11)

The determinant of 119869 is equal to

det (119869) = 120588 (120588 minus 120575) gt 0 (12)

while the trace of 119869 is equal to

trace (119869) = 120588 gt 0 (13)

which implies that (119875lowast 120587lowast) is an unstable equilibrium Itis possible to show that this system admits three moreequilibria namely (0 0) (119875lowast 0) and (0 120587lowast) Among them(0 0) and (0 120587lowast) are locally asymptotically stable

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] C Colapinto ldquoMoving to a multichannel and multiplatformcompany in the emerging and digital media ecosystem the caseof mediaset grouprdquo International Journal on Media Manage-ment vol 12 no 2 pp 59ndash75 2010

[2] TWeinbergTheNewCommunity RulesMarketing on the SocialWeb OrsquoReilly Media Inc Sebastopol Calif USA 2009

[3] C Colapinto and E Benecchi ldquoMovie industry goes viral inthe XXIst century if what counts is the buzzrdquo in CrossmediaInnovations I Ibrus and C A Scolari Eds pp 161ndash178 PeterLang Berlin Germany 2012

[4] C Colapinto and E Benecchi ldquoThe presentation of celebritypersonas in everyday twittering managing online reputationsthroughout a communication crisisrdquo Media Culture amp Societyvol 36 pp 219ndash233 2014

[5] A Toffler Future Shock William Morrow and Company NewYork NY USA 1980

[6] L Kung Strategic Management in the Media SAGE LondonUK 2008

[7] M PMcAllister and J Turrow ldquoNewmedia and the commercialsphere two intersecting trends five categories of concernrdquoJournal of Broadcasting amp Electronic Media vol 46 no 4 pp505ndash514 2002

[8] W S McDowell ldquoIssues in Marketing and Brandingrdquo in Hand-book of Media Management and Economics A B Albarran SM Chan-Olmsted and M O Wirth Eds pp 229ndash250 LEANew Jersey NJ USA 2006

[9] E Katz and P F Lazarsfeld Personal Influence The Free PressNew York NY USA 1955

[10] R Ando and A Marinelli ldquoFare ricerca sul fandom on line Ifan italiani e le serie tvrdquo in Sociologia 20 Pratiche Sociali eMetodologie di Ricerca sui Media Partecipativi S Monaci andB Scifo Eds 2010 Scriptaweb httpscriptawebeuCatalogosociologia-2-0

[11] A de Kosnik ldquoShould fan fiction be freerdquo Cinema Journal vol48 no 4 pp 118ndash124 2009

[12] C Sandvoss Fans Polity Press Cambridge UK 2005[13] I Askwith TV 20 turning television into an engagement

medium [MS thesis] 2007 httpcmsmiteduresearchthesesIvanAskwith2007pdf

[14] P BoothDigital Fandom NewMedia Studies Peter Lung 2010[15] J Caldwell ldquoCritical industrial practice branding repurposing

and the migratory patterns of the industrial textsrdquo Television ampNew Media vol 7 pp 99ndash104 2006

[16] H Jenkins S Ford and J Green Spreadable Media NYU NewYork NY USA 2013

[17] E Benecchi and G Richeri ldquoTv to talk about engaging withAmerican tv series through the internetrdquo inThe New TelevisionEcosystem A Abbruzzese and L Fortunato Eds Peter LangBern Switzerland 2013

[18] J T Caldwell Production Culture Duke University PressDurham NC USA 2008

[19] H Jenkins Convergence Culture Where Old and New MediaCollide New York University Press New York NY USA 2006

Abstract and Applied Analysis 9

[20] M Hills Fan Cultures Routledge London UK 2003[21] N Baym Personal Connections in the Digital Age Polity Press

Cambridge UK 2000[22] I Condry ldquoCultures of music piracy an ethnographic com-

parison of the US and Japanrdquo International Journal of CulturalStudies vol 7 pp 343ndash363 2004

[23] AAustinH Jenkins J Green I Askwith and S Ford ldquoTurningpirates into loyalists the moral economy and an alternativeresponse to file sharingrdquo Tech Rep MIT Convergence CultureConsortium Cambridge UK 2006

[24] D Boyd Facebookrsquos Little Gifts Apophenia 2007[25] H Jenkins ldquoLook ListenWalk Technologyrdquo 2004 httpwww

technologyreviewcomInfoTechwtr 13560[26] M Scaglioni TV di culto La Serialita Televisiva Americana e il

Suo Fandom Vita e Pensiero Milano Italy 2006[27] L Porter and D Lavery ldquoCultivating a lost audience the part-

icipatory fan culture of lostrdquo in Unlocking the Meaning ofLost An Unauthorized Guide L Porter and D Lavery EdsSourcebooks Naperville Ill USA 2006

[28] C Hoskins and R Mirus ldquoReasons for the US dominanceof the international trade in television programmesrdquo MediaCulture and Society vol 10 pp 499ndash515 1988

[29] C Colapinto E Sartori andM Tolotti ldquoAwareness persuasionand adoption enriching the bassmodelrdquo Physica A vol 395 pp1ndash10 2014

[30] A Bucci C Colapinto M Forster and D la Torre ldquoStochastictechnology shocks in an extended Uzawa-Lucas model closed-form solution and long-run dynamicsrdquo Journal of EconomicsZeitschrift fur Nationalokonomie vol 103 no 1 pp 83ndash99 2011

[31] V Capasso R Engbers and D la Torre ldquoOn a spatial Solowmodel with technological diffusion and nonconcave productionfunctionrdquo Nonlinear Analysis Real World Applications vol 11no 5 pp 3858ndash3876 2010

[32] D la Torre and S Marsiglio ldquoEndogenous technologicalprogress in a multi-sector growth modelrdquo Economic Modellingvol 27 no 5 pp 1017ndash1028 2010

[33] D Bielby and C HarringtonGlobal TV NYU Press New YorkNY USA 2008

[34] C Tosenberger ldquoSaving people hunting thingsrdquo TransformativeWorks and Culture vol 4 2010

[35] H Jenkins ldquoSupernatural first impressionsrdquo Confessions of anACA-fan 2007 httphenryjenkinsorg200701supernaturalhtml

[36] L Zubernis and K Larsen Eds Fan Phenomena SupernaturalIntellect Books Bristol UK 2014

[37] M Wilson ldquoCW Exec Professes Support for Supernaturalrdquo2008 httpscifiaboutcomb20080122cw-exec-professes-support-for-supernaturalhtm

[38] T Goodman ldquoWomenrsquosMurder Club-bonding over crimerdquo SanFrancisco Chronicle October 2007

[39] A Stanley ldquoHomicide and Heelsrdquo The New York TimesOctober 2007

[40] Informa Telecoms and Media ldquoWorld most popular showsrdquoRadio Times August 2006

[41] ldquoAuditel datardquo httpwwwauditelit[42] H E Kunze D la Torre and E R Vrscay ldquoInverse problems

for random differential equations using the collage method forrandom contraction mappingsrdquo Journal of Computational andApplied Mathematics vol 223 no 2 pp 853ndash861 2009

[43] H Kunze D la Torre and E R Vrscay ldquoA generalized collagemethod based upon the Lax-Milgram functional for solvingboundary value inverse problemsrdquo Nonlinear Analysis TheoryMethods amp Applications vol 71 no 12 pp e1337ndashe1343 2009

[44] R Picard The Economics and Financing of Media CompaniesFordham University Press 2002

[45] M R Caputo Foundations of Dynamic Economic Analysis Opti-mal Control Theory and Applications Cambridge UniversityPress 2005

[46] T A Weber Optimal Control Theory with Applications inEconomics The MIT Press Cambridge Mass USA 2011

[47] H Jenkins Fans Bloggers and Gamers Media Consumer in theDigital Age Routledge London UK 2007

[48] E Benecchi andCColapinto ldquoEngagingwithGlee Transmediastorytelling for a television in transitionrdquo in Proceedings ofthe 25th International Conference of Communication (BusinessModels for a Digital Economy The Value of Contents) 2010

[49] J-C Rochet and J Tirole ldquoPlatform competition in two-sidedmarketsrdquo Journal of the European Economic Association vol 1no 4 pp 990ndash1029 2003

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

8 Abstract and Applied Analysis

The Hamiltonian associated with model (5) is

119867(119875 (119905) 120587 (119905)) = ln (120587 (119905)) 119890minus120588119905 + 120582 (119905)

times (minus120575119875 (119905) + (Ω119875 (119905) minus 120587 (119905)) 119875 (119905))

(6)

Optimality conditions for (6) read as

0 =

120597119867

120597120587

=

119890

minus120588119905

120587 (119905)

minus 120582 (119905) 119875 (119905)

minus

120582 (119905) =

120597119867

120597119875

= 120582 (119905) (minus120575 + 2Ω119875 (119905) minus 120587 (119905))

119875 (119905) =

120597119867

120597120582

= minus120575119875 (119905) + (Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

(7)

The system (7) is equivalent to

120587 (119905) =

119890

minus120588119905

120582 (119905) 119875 (119905)

997904rArr

(119905)

120587 (119905)

= minus120588 minus

120582 (119905)

120582 (119905)

minus

119875 (119905)

119875 (119905)

minus

120582 (119905) = 120582 (119905) (minus120575 + 2Ω119875 (119905) minus 120587 (119905))

997904rArr minus

120582 (119905)

120582 (119905)

= minus120575 + 2Ω119875 (119905) minus 120587 (119905)

119875 (119905) = minus120575119875 (119905) + (Ω119875 (119905) minus 120587 (119905)) 119875 (119905)

997904rArr

119875 (119905)

119875 (119905)

= minus120575 + Ω119875 (119905) minus 120587 (119905)

(8)

which implies

(119905)

120587 (119905)

= minus120588 + Ω119875 (119905)

119875 (119905)

119875 (119905)

= minus120575 + Ω119875 (119905) minus 120587 (119905)

(9)

The only nontrivial equilibrium is

119875

lowast=

120588

Ω

120587

lowast= 120588 minus 120575 gt 0

(10)

The Jacobian of the linearized system at (119875lowast 120587lowast) is equal to

119869 = [

0 Ω (120588 minus 120575)

minus

120588

Ω

120588

] (11)

The determinant of 119869 is equal to

det (119869) = 120588 (120588 minus 120575) gt 0 (12)

while the trace of 119869 is equal to

trace (119869) = 120588 gt 0 (13)

which implies that (119875lowast 120587lowast) is an unstable equilibrium Itis possible to show that this system admits three moreequilibria namely (0 0) (119875lowast 0) and (0 120587lowast) Among them(0 0) and (0 120587lowast) are locally asymptotically stable

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] C Colapinto ldquoMoving to a multichannel and multiplatformcompany in the emerging and digital media ecosystem the caseof mediaset grouprdquo International Journal on Media Manage-ment vol 12 no 2 pp 59ndash75 2010

[2] TWeinbergTheNewCommunity RulesMarketing on the SocialWeb OrsquoReilly Media Inc Sebastopol Calif USA 2009

[3] C Colapinto and E Benecchi ldquoMovie industry goes viral inthe XXIst century if what counts is the buzzrdquo in CrossmediaInnovations I Ibrus and C A Scolari Eds pp 161ndash178 PeterLang Berlin Germany 2012

[4] C Colapinto and E Benecchi ldquoThe presentation of celebritypersonas in everyday twittering managing online reputationsthroughout a communication crisisrdquo Media Culture amp Societyvol 36 pp 219ndash233 2014

[5] A Toffler Future Shock William Morrow and Company NewYork NY USA 1980

[6] L Kung Strategic Management in the Media SAGE LondonUK 2008

[7] M PMcAllister and J Turrow ldquoNewmedia and the commercialsphere two intersecting trends five categories of concernrdquoJournal of Broadcasting amp Electronic Media vol 46 no 4 pp505ndash514 2002

[8] W S McDowell ldquoIssues in Marketing and Brandingrdquo in Hand-book of Media Management and Economics A B Albarran SM Chan-Olmsted and M O Wirth Eds pp 229ndash250 LEANew Jersey NJ USA 2006

[9] E Katz and P F Lazarsfeld Personal Influence The Free PressNew York NY USA 1955

[10] R Ando and A Marinelli ldquoFare ricerca sul fandom on line Ifan italiani e le serie tvrdquo in Sociologia 20 Pratiche Sociali eMetodologie di Ricerca sui Media Partecipativi S Monaci andB Scifo Eds 2010 Scriptaweb httpscriptawebeuCatalogosociologia-2-0

[11] A de Kosnik ldquoShould fan fiction be freerdquo Cinema Journal vol48 no 4 pp 118ndash124 2009

[12] C Sandvoss Fans Polity Press Cambridge UK 2005[13] I Askwith TV 20 turning television into an engagement

medium [MS thesis] 2007 httpcmsmiteduresearchthesesIvanAskwith2007pdf

[14] P BoothDigital Fandom NewMedia Studies Peter Lung 2010[15] J Caldwell ldquoCritical industrial practice branding repurposing

and the migratory patterns of the industrial textsrdquo Television ampNew Media vol 7 pp 99ndash104 2006

[16] H Jenkins S Ford and J Green Spreadable Media NYU NewYork NY USA 2013

[17] E Benecchi and G Richeri ldquoTv to talk about engaging withAmerican tv series through the internetrdquo inThe New TelevisionEcosystem A Abbruzzese and L Fortunato Eds Peter LangBern Switzerland 2013

[18] J T Caldwell Production Culture Duke University PressDurham NC USA 2008

[19] H Jenkins Convergence Culture Where Old and New MediaCollide New York University Press New York NY USA 2006

Abstract and Applied Analysis 9

[20] M Hills Fan Cultures Routledge London UK 2003[21] N Baym Personal Connections in the Digital Age Polity Press

Cambridge UK 2000[22] I Condry ldquoCultures of music piracy an ethnographic com-

parison of the US and Japanrdquo International Journal of CulturalStudies vol 7 pp 343ndash363 2004

[23] AAustinH Jenkins J Green I Askwith and S Ford ldquoTurningpirates into loyalists the moral economy and an alternativeresponse to file sharingrdquo Tech Rep MIT Convergence CultureConsortium Cambridge UK 2006

[24] D Boyd Facebookrsquos Little Gifts Apophenia 2007[25] H Jenkins ldquoLook ListenWalk Technologyrdquo 2004 httpwww

technologyreviewcomInfoTechwtr 13560[26] M Scaglioni TV di culto La Serialita Televisiva Americana e il

Suo Fandom Vita e Pensiero Milano Italy 2006[27] L Porter and D Lavery ldquoCultivating a lost audience the part-

icipatory fan culture of lostrdquo in Unlocking the Meaning ofLost An Unauthorized Guide L Porter and D Lavery EdsSourcebooks Naperville Ill USA 2006

[28] C Hoskins and R Mirus ldquoReasons for the US dominanceof the international trade in television programmesrdquo MediaCulture and Society vol 10 pp 499ndash515 1988

[29] C Colapinto E Sartori andM Tolotti ldquoAwareness persuasionand adoption enriching the bassmodelrdquo Physica A vol 395 pp1ndash10 2014

[30] A Bucci C Colapinto M Forster and D la Torre ldquoStochastictechnology shocks in an extended Uzawa-Lucas model closed-form solution and long-run dynamicsrdquo Journal of EconomicsZeitschrift fur Nationalokonomie vol 103 no 1 pp 83ndash99 2011

[31] V Capasso R Engbers and D la Torre ldquoOn a spatial Solowmodel with technological diffusion and nonconcave productionfunctionrdquo Nonlinear Analysis Real World Applications vol 11no 5 pp 3858ndash3876 2010

[32] D la Torre and S Marsiglio ldquoEndogenous technologicalprogress in a multi-sector growth modelrdquo Economic Modellingvol 27 no 5 pp 1017ndash1028 2010

[33] D Bielby and C HarringtonGlobal TV NYU Press New YorkNY USA 2008

[34] C Tosenberger ldquoSaving people hunting thingsrdquo TransformativeWorks and Culture vol 4 2010

[35] H Jenkins ldquoSupernatural first impressionsrdquo Confessions of anACA-fan 2007 httphenryjenkinsorg200701supernaturalhtml

[36] L Zubernis and K Larsen Eds Fan Phenomena SupernaturalIntellect Books Bristol UK 2014

[37] M Wilson ldquoCW Exec Professes Support for Supernaturalrdquo2008 httpscifiaboutcomb20080122cw-exec-professes-support-for-supernaturalhtm

[38] T Goodman ldquoWomenrsquosMurder Club-bonding over crimerdquo SanFrancisco Chronicle October 2007

[39] A Stanley ldquoHomicide and Heelsrdquo The New York TimesOctober 2007

[40] Informa Telecoms and Media ldquoWorld most popular showsrdquoRadio Times August 2006

[41] ldquoAuditel datardquo httpwwwauditelit[42] H E Kunze D la Torre and E R Vrscay ldquoInverse problems

for random differential equations using the collage method forrandom contraction mappingsrdquo Journal of Computational andApplied Mathematics vol 223 no 2 pp 853ndash861 2009

[43] H Kunze D la Torre and E R Vrscay ldquoA generalized collagemethod based upon the Lax-Milgram functional for solvingboundary value inverse problemsrdquo Nonlinear Analysis TheoryMethods amp Applications vol 71 no 12 pp e1337ndashe1343 2009

[44] R Picard The Economics and Financing of Media CompaniesFordham University Press 2002

[45] M R Caputo Foundations of Dynamic Economic Analysis Opti-mal Control Theory and Applications Cambridge UniversityPress 2005

[46] T A Weber Optimal Control Theory with Applications inEconomics The MIT Press Cambridge Mass USA 2011

[47] H Jenkins Fans Bloggers and Gamers Media Consumer in theDigital Age Routledge London UK 2007

[48] E Benecchi andCColapinto ldquoEngagingwithGlee Transmediastorytelling for a television in transitionrdquo in Proceedings ofthe 25th International Conference of Communication (BusinessModels for a Digital Economy The Value of Contents) 2010

[49] J-C Rochet and J Tirole ldquoPlatform competition in two-sidedmarketsrdquo Journal of the European Economic Association vol 1no 4 pp 990ndash1029 2003

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Abstract and Applied Analysis 9

[20] M Hills Fan Cultures Routledge London UK 2003[21] N Baym Personal Connections in the Digital Age Polity Press

Cambridge UK 2000[22] I Condry ldquoCultures of music piracy an ethnographic com-

parison of the US and Japanrdquo International Journal of CulturalStudies vol 7 pp 343ndash363 2004

[23] AAustinH Jenkins J Green I Askwith and S Ford ldquoTurningpirates into loyalists the moral economy and an alternativeresponse to file sharingrdquo Tech Rep MIT Convergence CultureConsortium Cambridge UK 2006

[24] D Boyd Facebookrsquos Little Gifts Apophenia 2007[25] H Jenkins ldquoLook ListenWalk Technologyrdquo 2004 httpwww

technologyreviewcomInfoTechwtr 13560[26] M Scaglioni TV di culto La Serialita Televisiva Americana e il

Suo Fandom Vita e Pensiero Milano Italy 2006[27] L Porter and D Lavery ldquoCultivating a lost audience the part-

icipatory fan culture of lostrdquo in Unlocking the Meaning ofLost An Unauthorized Guide L Porter and D Lavery EdsSourcebooks Naperville Ill USA 2006

[28] C Hoskins and R Mirus ldquoReasons for the US dominanceof the international trade in television programmesrdquo MediaCulture and Society vol 10 pp 499ndash515 1988

[29] C Colapinto E Sartori andM Tolotti ldquoAwareness persuasionand adoption enriching the bassmodelrdquo Physica A vol 395 pp1ndash10 2014

[30] A Bucci C Colapinto M Forster and D la Torre ldquoStochastictechnology shocks in an extended Uzawa-Lucas model closed-form solution and long-run dynamicsrdquo Journal of EconomicsZeitschrift fur Nationalokonomie vol 103 no 1 pp 83ndash99 2011

[31] V Capasso R Engbers and D la Torre ldquoOn a spatial Solowmodel with technological diffusion and nonconcave productionfunctionrdquo Nonlinear Analysis Real World Applications vol 11no 5 pp 3858ndash3876 2010

[32] D la Torre and S Marsiglio ldquoEndogenous technologicalprogress in a multi-sector growth modelrdquo Economic Modellingvol 27 no 5 pp 1017ndash1028 2010

[33] D Bielby and C HarringtonGlobal TV NYU Press New YorkNY USA 2008

[34] C Tosenberger ldquoSaving people hunting thingsrdquo TransformativeWorks and Culture vol 4 2010

[35] H Jenkins ldquoSupernatural first impressionsrdquo Confessions of anACA-fan 2007 httphenryjenkinsorg200701supernaturalhtml

[36] L Zubernis and K Larsen Eds Fan Phenomena SupernaturalIntellect Books Bristol UK 2014

[37] M Wilson ldquoCW Exec Professes Support for Supernaturalrdquo2008 httpscifiaboutcomb20080122cw-exec-professes-support-for-supernaturalhtm

[38] T Goodman ldquoWomenrsquosMurder Club-bonding over crimerdquo SanFrancisco Chronicle October 2007

[39] A Stanley ldquoHomicide and Heelsrdquo The New York TimesOctober 2007

[40] Informa Telecoms and Media ldquoWorld most popular showsrdquoRadio Times August 2006

[41] ldquoAuditel datardquo httpwwwauditelit[42] H E Kunze D la Torre and E R Vrscay ldquoInverse problems

for random differential equations using the collage method forrandom contraction mappingsrdquo Journal of Computational andApplied Mathematics vol 223 no 2 pp 853ndash861 2009

[43] H Kunze D la Torre and E R Vrscay ldquoA generalized collagemethod based upon the Lax-Milgram functional for solvingboundary value inverse problemsrdquo Nonlinear Analysis TheoryMethods amp Applications vol 71 no 12 pp e1337ndashe1343 2009

[44] R Picard The Economics and Financing of Media CompaniesFordham University Press 2002

[45] M R Caputo Foundations of Dynamic Economic Analysis Opti-mal Control Theory and Applications Cambridge UniversityPress 2005

[46] T A Weber Optimal Control Theory with Applications inEconomics The MIT Press Cambridge Mass USA 2011

[47] H Jenkins Fans Bloggers and Gamers Media Consumer in theDigital Age Routledge London UK 2007

[48] E Benecchi andCColapinto ldquoEngagingwithGlee Transmediastorytelling for a television in transitionrdquo in Proceedings ofthe 25th International Conference of Communication (BusinessModels for a Digital Economy The Value of Contents) 2010

[49] J-C Rochet and J Tirole ldquoPlatform competition in two-sidedmarketsrdquo Journal of the European Economic Association vol 1no 4 pp 990ndash1029 2003

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of