1961 Experimental Games and Bargaining Theory

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Experimental Games and Bargaining TheoryAuthor(s): T. C. SchellingReviewed work(s):Source: World Politics, Vol. 14, No. 1, The International System: Theoretical Essays (Oct.,1961), pp. 47-68

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EXPERIMENTAL GAMES

AND BARGAINING THEORY

ByT. C. SCHELLING

GMES havebeenused n thestudyfinternationalolitics;ftheywerenot so demanding f timeand energy,heywould

probably eusedmore.A Berlin risis, r a busyday n the ifeoftheUnitedNations, ends itself o thisprocedure. articipants suallyrepresentcountries"nd theymaybe encouraged o playthe"role"of thecountry,cting s theybelieve hecountry ould act,or theymaybe encouragedo behave nthegameas they elieve hecountryought obehave n itsown interest.he gamemaybe organizedforresearch,heparticipantseingscholars nd policy nalysts; r itmaybe organized s training,o givestudents icarious xperiencen thecomplexitiesfinternationalolitics.

And complexities re preciselywhat the game usuallygenerates.Gamesorganized or hebenefitfstudents reinvariablyeporteds

having penedtheir yes,n an unprecedenteday,to the varietiesfchoicethat an confrontations, o thevarietiesfinterpretationhatcan be puton a country'sehavior, o thegreatcloak of detailthatsurroundsven thesimplestnternationalrisis,nd to the imitationsonformalheorys a guide to nternationalonductn therealworld.These complexitiesmotivate,oo, thegamesorganized o examineproblematherhantoraise he ophisticationf a student; artoftherationale f game organizations thatno straightforwardnalytical

processwillgenerate "solution" o theproblem, redict n outcome,orproduce comprehensive apofthe lternativeoutes,rocesses,ndoutcomeshat re atent ntheproblem.

Gamesdo generatehese omplexitiesnd,by mostreports, o it ina fruitfulnd stimulating ay. If an understandingf internationalpolitics equires amiliarity ithboththeoryndpractice,usygamesseem oprovide n importantouch fpractice. utthough heymaybe peculiarlyuitable orbringing ut the richcomplexityf interna-

tionalprocesses,amesare not imitedn principle o that nd ofthescale.Frequent eferencesochessremind s thatmore ustere amesmaybe useful n the study f bilateral r multilateralonflict.hemoreabstractnd stylized amecan certainlyotpretend o providevicariousxperiencen thepractice finternationalolitics, ut tmayhavea role nthe heory.







48 THE INTERNATIONAL SYSTEM

A gamemaybe useful n revealinghestructuref conflictsatherthanthedetails.A gamemaybe useful n the articulationf a theo-reticalmodel f t is designed or hatpurpose,ustas gamesrichern

detailmayhelpto fit heorynto ts nstitutionalontext. he purposesdo notnecessarilyompetewith each other,nordo thegames. t isworthwhileo examinenternationaloliticsn all itscomplexity,ndworthwhile o examinethe underlyingtructurey the use of anabstractmodel.Similarly, amesmay be helpful t either nd of thespectrum,rinbetween.

The methodology ill be different,hough.One kindof gamemaybe usedtoelucidate theoretical odel, he ther oshow ts imitations.One may be used to bringout the order,the rationality,nd thecoherence f the internationaltructure; he other to illustrate hedisorder,he rrationality,nd the ncoherence.ependingon thepur-pose and what is to be emphasized, ne notonlydesigns hegamedifferentlyut definesthe purpose differently.ne can questionwhethern experimentalameservesn essential urpose, revenanyuseful urpose,oward he nd ofthe pectrumhat an beencompassed

bya theoretical odel.Toward theother nd,wheretheorymeets tslimitations,omeneedtogenerate "sample"ofvicarious xperiencemayseemto be compelling; ut thehaphazardquality fgameplay-ing,while helpful n supplementingheoreticalmodels,might eemto be precisely hatone wantsto eliminaten examining hetheoryitself.

The questions a soundone,but tdoes admit n answer. ven themost ustere nd economical heoretical odel s unlikely obe fully

determinate.t will be too complexto yieldto any straightforwardcomprehensivenalysis.t is not usually mathematicalroblem obe "solved," ut a modelthatgenerates varietyfpotential ehaviorevenwithin heframeworkfa fewvariablesndconstraints.urther-more, mongtheprocesseshat t leaves ndeterminateill be somethat nherentlynvolve he nteractionftwo ormoredecision enters.

Forthis eason hereslikely obe,evenwithin he implified odel,

some copefor freectivity,"orbargaining,or hereaching funder-standingsndmisunderstandings,or ccommodationndco-operation,andfor onjecturesbout achother's ecision rocesses, aluesystems,and information.he theoretical odel s thususuallynot a compre-hensivepecificationfhowtheparticipantsehave, utrather specifi-cationoftheframework ithinwhichtheypursuecertain bjectivesaccording o certain riteria.What the model leads to in terms f







GAMES AND BARGAININGTHEORY 49

behaviorf theparticipantss usually eyondhereach fstraight-forwardnalysis.

Even f t snot, hegame tself ay e a fruitfulayofdeveloping

a workingcquaintanceith theoreticaltructure.ustesigninghegame, heckingt fornternalonsistencyndforwhethertcontainsthe ssentialsf thedesiredheoreticalodel,an be a usefulxerciseandsometimescheck nthe onsistencyf he onceptsn themodel.The gamefurthermorerovidesn extensiveefinitionfthetermsofthe heory,ndmay acilitateommunicationndcomparison.necanpoint ophenomenahat hegamegenerates,ndnotbe limitedtoabstractharacterizationsfwhat ehas nmind.

But hegame ango onestep arther. theoreticalodel ften asthe haracteristichatt s notformallyrmathematicallyeterminateofbehaviorvenforfully ational articipantshounderstandhegame. he reasonsthat,monghephenomenaf nternationaloli-tics hat theoryants oelucidate,re heprocessesfunderstandingandmisunderstanding.hetheory ay hereforeant oleave copeformisunderstandings,s well sunderstandings;nd game esignedtocorrespondo the heoryillwant o

provideor ehaviorhat an

lead ounderstandingsndmisunderstandings.nd heresnostraight-forwarday, oformalnalyticalay, or rdinaryrational"nalysisto nticipatehe utcome.hereasonssimple:ttakes wo omakemisunderstanding.

Considern example. theoreticalodel ermitsertain inds fcommunication;orrespondingly,theoreticallyrientedame ermitsthe ransmittalfmessages.ow canwediscoverhevarious ays n

which messagemaybemisinterpreted?eep nmind hat hemis-interpretationshat he enderf messageanperceivendanticipate,he canguard gainst; heonesthatmatter ost rethose e cannotperceivenadvance.hequestionhen ecomes,owdo we dentifyhepossiblenterpretationsf a messagehat id notoccur o thepersonwho entt?Puttingtmore rudely,ndmore enerally,owcan ananalystrawup a listof the hingshatwouldnever ccur ohim?Ifthe ssencef he ames that herere wo rmore eparateartici-

pants,woor more entersfconsciousnessndofdecision, e cangeneratenderstandingsnd misunderstandings.hus the"game"formulationf the heorys a meaningfulne; it cancontainome-thingssentialo the heory.ndtostudyt nrelationothe heory-ina sufficientlybstract odel opermitheoreticalandling,nd theisolationfcriticalariables-anustere,bstract,tylized,heoreticalgamemay ave use.








I. A GAME FORTHE STUDY OF THEORY

This paperis about such a game, n a research roject ustbeinginitiated.t is an experimentaltudy fthebargaining rocessnvolvedin limitedwarand other onflicts,processn whichbargainings bymaneuvers much s bywords,nwhich ommunicationspoor, egalenforcements unavailable, nd the participantsmake irreversiblemoveswhilethey argain, reuncertainbouteachother's alues, ndhave somepowerto inflict ratuitousamageon each other.The re-searchwill utilizevariantsf an experimentalame.

The game in its present ormbearsno particular esemblanceowar. It does use a map,but so do a lot of children's

ames.tmayremind ne ofthegamethat oesunder henameof"Salvo" or "Battle-

ship,"nwhich achplayer laceshisships n a set fsquares nd takesturns iring t theother's hipswhosewhereabouts e can learnonlywhentheother eports hit.Buttheresa differenceetweenhegameproposed ere ndthefamiliarwo-personarlor ames.

The differencesthat wo-personarlor ames realways zero-sum"games-gamesofpureconflictn whichone'sgain is theother'soss.

Mutualgain and mutual oss are out of thequestion;and bargains,threats,nd co-operation-evenrudging o-operation-cannotccurif bothplayers nderstandhegameandplay to win. n thegame pro-posed here that s notso. Someoutcomes re better orboth playersthan thersndtheplayerstobemotivatedo getthehighestbsolutescoreforhimself,otto impose low scoreon an opponent,nd nottoconcern imself ithhisrelative core.

The fundamentaldea is thatwar-whether "fighting" ar or a

process f strategic aneuver-isnot a zero-sum ame. It requires tleast ome o-operationraccommodationetween he wosides. t is a"bargainingituation,"n whichtheconflictnd the nterdependenceare nseparable.Whilesecrecymayplaya role, t susuallynecessaryorevealpreferenceso reachefficientrades nd compromises,omakethreatsredible,nd todemonstratenabilityocomplywithproposalsand threats.t is importanto mpress n theopponentpartner) ometruthbout one'sownmode ofbehavior. ommunicatingne's inten-

tions ndwhatoneexpects f theother s importantosuccessfullay,and isnecessarilypreoccupationf theplayers. he players rebothpartnersnd adversaries,s concerned o avoidseveremutualdamageas togainat theexpense feachother.

This kind ofsituationoesnotarise n thetraditionalarlorgames.'1The reasonprobablys thatnon-zero-sumames re no fununless ctualrewards

areprovided-i.e., nless hepartnerscompetitors,ivals)can ointly eatthe "house."








This swhy game ikechess asonly limitedelevances a "wargame."f onewants ostudyn actual arlor-typeame-anabstract,formalizedame-toget nsightnto hestrategyf limited aror

the trategyfthreats,eprisals,eterrence,ndbargaining,hererenoready-madeamesvailable.t hasbeennecessaryo nventgame.Thegame sedn his esearchasbeen esignedorequireo-ordina-

tion fstrategiesndtomake o-ordinationifficult.t has beende-signed omaketdifficulto dentifynobviouslyfair"rsymmetricaloutcome.thasbeendesignedorequire osignificantechnicalkillthat astobeacquiredhroughepeatedlays. he skill nvolvedsintendedo be morekin obargainingkills,trategicngenuity,kill

in coercingn opponent,ather han kill n themechanicsf thegame tself.Thegamediffersromraditionalargamesntworespects.irst,

virtuallyllwargames avebeen itherxplicitlyrimplicitlyzero-sum"games. heyhave nvolvedo scope or ollaborationetweentheadversaries;nymotivationoward winning" as beentowardwinningver heopponent,utdoingheopponent,inningelativetotheopponentexcept otheextenthat,s in tennis,nemaybe

interestedndisplayingtyleswell s inwinning).econd,his ameis notdesignedolookmuch ikewar; itis designed orminimumtechnicalomplexity.t is designedorresearchatherhan raining.(It doesappear,hough,ohavesome mportantalue n thecom-municationf deas.) t isdesignedohave simplenoughtructure,andfewenough ariablesnd parameters,o permitmeasurement,classification,anipulation,ndanalysis,n accordance ith theo-reticalramework.t isalsodesignedobeeconomicalnthe nterestofrepeatedlays,ndtobecapable freproductionithoutccess ouniquematerials.

It should e emphasizedhatnthis ameplayersresupposedoplay owin.Whilensome ariantshere illbe a scenariondotherdetailsuggestivefsome real" ituation,t snot ntendedhat ub-jects lay ny uch ersionf t na "role-playing"ense. heplayersarenot o mitateecision-makersnsome eal ituationhat hegame

istryingomimic.orthepurposefthis ame,ncontrastocertainverydifferent-lookingnd lessstylized ar gamesand,especially,"politicalames,"ne splayingomaximizeis corendnotfor nyotherurpose.2

Thisposes problem.layers aveto interesthemselvesn theirabsolutecores, ot ust n howwellthey eatan adversary. hile

2 See note7 at theendofthepaperforreferenceso other xperimentalames.








competitivepiritspreciselyhat ne wantsnstudying zero-sumgame,ikemost arlor ames,nd canusually e relied n tomakepeoplevaluepreciselyhe kindof score hey re supposedo be

maximizing,tcannot e relied ntomakepeoplenterestedntheirabsolutecoresn a two-personame.Money ewardsrethereforeused,both o appealto profitmotivesnd to dramatize hepayoffstructuref hegame ndtoattachymbolicalue o t.

II. A DESCRIPTION OF THE GAME AND ITS STATE OF DEVELOPMENT

A gamehasbeen eveloped.tinvolvesboard nda set fchips rcounters.heboard s n theformf map;themap npresentse ssimplyn outlinemapof theUnited tates,he48 states eing heunits ntowhich hemap s divided.3ach ofthetwoplayers asasupplyfchips; teachplay hey lace hips nthe tatesnd removethem,ubjectocertainimitations.hen he amesover,he layers'scores epend nthe tateshey ossessndthechips hey ave ost,andanyotherdamage"hey ave uffered.he states avedifferentvalues; heir alues,urthermore,ifferor he woplayers,ndwhileeachplayer nowshevalues ohimselffthedifferent

tates,e haslittle nowledgefhisopponent'salue ystem.achdoeshavefullknowledgefthe ther'sastmoves. hips re ostbytheprocessf"fighting"or tates;ther amage anbesufferedecauseachplayerhas,among hemoves vailable ohim, ne that s purely unitiveinnature. hegamesterminatedhen oth layersgree ostop.Nocommunicationsallowed etweenhe woplayers.

Thegamesessentiallyne f bargainingymaneuver,"f ignaling

intentions,roposals,hreats,efusals,nd informationboutone'spreferenceshrough aneuveratherhanhroughords.Thegame scompletelyefinedy set f nstructionsndthemap.

The most ecentersionfthe nstructionssappendedothis aper.Thegame n tspresentorm sually uns or fewhours.ttakes

about n hour fpreliminarynstructiono geta player onversantwith he echnicaleaturesfthegame ndtoemphasizehe deathathe splayingor nabsolutendnot relativecore; arlynthegame

a player ecomesware fthepossibilityfsignalingnd its mpor-tance,ndbegins heprocessfworkinguta "language" ithhisopponentpartner)ndofdevelopingfewnotionsbout trategy.Formost fthosewhohaveplayedt,thegamehasproved o beengrossingndstimulating.Withmoderatedaptationfthe ulestcanbemade three-person3A I958 mapof48 statess used.








orfour-personame.Withnochangenthe ules,tcan beplayed yteams atherhanpersons.

The physicalequirementsf thegameare modest-agood-sized

table ohold womapsmeasuringbout 0 X 30 inches, ith barrierbetweenokeep heplayersromeeing achother'smaps ndeachother'saces,ogetherith monitor ho canseebothmaps t thesame ime. lternativelyhe layersanbeonoppositeides f room;withoutoomuch uisanceheyould ommunicatey elephone.orteam lay, hererivacyfconversationould erequired,wo oomsorbooths ould eneeded,ut elephoneommunicationtwomoni-torswith n opentelephoneinebetween)wouldpermitomeflex-ibilitynlocation.

There re everaleaturesf hegame hat anbe varied. hevaluesof he tatesanbevaried,articularlyhe orrelationetweenhe woplayers'alue ystems,.e., he egreefpotentialonflictnthe xerciseof their references.he informationhat achhasabout he other'svalue ystemanbevaried. he communicationystemanbevaried,throughhe dditionfsymmetricalr symmetricalrrangementsordirectommunication,itherree r restrictedocertainypesfstate-ments rproposals.hemapcanbe varied,oth ochange hegeo-metricalonfigurationnd tochangehepoliticalndother onnota-tions hatmay nfluencehebargainingrocess. scenario an beprovidedhatmay ave n mportantower f uggestion;layers ayormay ot egivennformationbout he utcomefpreviouslays fthe samegame-knowledge hichmayconstrainr facilitatehebargainingrocess.henumberf ountersanbevaried;nparticular,

thenumberf hipsvailableothe wo layersould iffer.hetempoofthegame anbeaffectedyvaryinghenumberfchips layed teach urn,ndbyrequiringhat he reaclaimed y player'ships eenlargednlyncrementally.herole freprisalrpunitivectionanbevaried,ithernthe osts f nflictingamage rby imitsnthenumberrfrequencyfpunitivemoves.Andnewmoves ndnewresourcesanbeadded othegame.Furtherefinementf he amewill akemainlyhe orm f dapting

thesetructuraleaturesndparameters.ariationill lso, owever,epart f he xperimenttself,o tudyhe ffectn themode fplay ndonthe utcome,ndontheplayers'nteractionith achother.

Furtherevelopmentf he amewill equirecompromise,etween(a) enrichinghe ame'somplexity,hevarietyfmovesvailable,hesuggestiveetails,he ommunicationtructure,tc.,ogeneratenterest-ingphenomena,nd (b) keeping hegame implenougho be not








only conomicalut usceptiblefanalysisn relationoa theoreticalmodel.

III. THEORY AND METHODOLOGY

The basicnotionnderlyingheuse of n experimentalame nanempiricaltudy f the"bargainingrocess"s thatformalheory-game heory,or xample-isnadequatey tself,ndnecessarilyo, nthe tudyfbargainingames.Games fthis ort ecessarilyontainanelementf ndeterminacy;he onstraintsmposedythe uantita-tive tructurefthegame re nsufficientodeterminesolution,venfor rational,"nternallyonsistent,trategiesfbehaviorytheparti-

cipants.nany ame f hisortheres some eed or he oncertingfaction,or eachingnderstandings,or ommunicatingnd nferringintentions,or rrivingtconsistentxpectationsf ach ther,ndforthedevelopmentfnorms,raditions,rotheronstraintsnalogousothe imitsn imited ar.Howtheparticipantsan nteracto teachsharedxpectation,ow hey an nvent eans f ignalingheirnten-tions, hat indsfrules nd raditionsheyanperceivendrecognizejointlyannot earrivedtby priorieasoning,ven y deallyational

players.heresanessentiallementf mpiricaltudynvolved.Thisis not, t should e emphasized,imply matter fplayers'behavingn practicen a manner ifferentromwhata theoryfrational ehaviorould uggest.athert sthat layersrecapable,tleastnsome ircumstances,fdoing gooddealbetterhan purelyformalheoryfrationalehaviorould ccountor. ow t sthatheycando betters a questionhat,houghmenableotheoreticalnalysis,ultimatelyequiresmpiricalonfirmation.

Thepossibleelevancefexperimentalork eems emonstratedysomeexperimentsithquestionnaireshatcanbe consideredone-move" on-zero-sumames.4heresearchnitiatedith his ewgamecanbevieweds anattempto dofor argainingxtendedver imewhat he uestionnaireidfor ne-shotames.

An importantuestions whetherheconclusionseached,r thephenomenabserved,anbegeneralizedocoverctual onflictitua-tions,ctualbargainingrocesses,fwhich imited armaybe themost ivid xample. ere tshould irstesaid hat game fthis ortis not ntendedoreproducell the ignificantharacteristicsfa realconflict;t s notntendedo pitomizeeal,ive onflictr oconstitute"well-balanced"odelnwhich ll elementseceiveropermphasis.

Reported n T. C. Schelling, Bargaining, ommunication,nd LimitedWar,"JournalfConflict esolution, (March 957), pp. i9-36; reprintedn Schelling, heStrategyfConflict,ambridge, ass., 960.








It s ntendedatherosingle ut spectsftheproblemhat rovidecoherentubjectornalysisnd re usceptiblefexperimentalimula-tion nthe aboratory.game f this ort ocusesmainlyntheper-

ceptual nd cognitiverocesses f theparticipants,ather han onemotionalehaviorr ndividualalue ystems.So far spossibleheplayer'salue ystems providedimby hegame tself;nd whileemotionalnvolvementsundoubtedlyresent,ven fwetryokeep tout, t s ona differentcale romhe uress,ension,reoccupation,ndpanic hatmightccurn real,ive onflictituation.)

Thegame urthermoreslimitedn tsrelevanceothebehaviorfindividualsor perhaps ery mallgroups) nd to those spects forganizationalehavior,ureaucraticehavior,roup oliticalehavior,andother ollectiveecision rocesseshatmostdepend n,or arelimitedy, he apabilitiesndcharacteristicsf ndividuals,rat leastinwhichhe apabilitiesndcharacteristicsf ndividualecisionroc-essesanbe solatednanalysis.Whatmakes game fthis ort,imiteds it s, ttractives a means

ofcomingogripswith ome spects f imited arand similaron-flictssthatwearepoor nalternativeays f tudyinghe henomenaempirically.e aregenerallyimitedo ntensivetudiesfa fewpar-ticularases. heknowledge e cangetfromxperimentingithgamemaynotbe comprehensiver terriblyeliable,ut, omparedwithwhatwehave rcangetnany ther ay,t ooks ood.There sanothereasonorupposinghat ven quite rtificialame

canproduceesultsfreal ignificance.greatmanyropositionsboutlimited ar,ndustrialisputes,tc., rephrasednsuch eneralerms,

and based nreasoningrevidencefsuch implicityndgenerality,that hey ouldhave oapply oa situations simplendartificialsthekindofgamedescribedbove. n otherwords, ven fwe areskepticalbouthe ropositionshat anbeprovedy he videncefgame fthis ort, gooddealofthe xistingheory,r ore,ssuscepti-bleofbeing isproved.

Consider,orexample,ropositionsbout headvantagerdisad-vantage f communicationetweendversariesn limitedwar,or

propositionsbout he endencyor ertainargainingrocessesodis-play utcomeshathave omepropertyf"equality"r "symmetry."Many fthese eem o be based nvery eneralbservationnd ntro-spection,xpressednphrasesike It standsoreasonhat . ." or"Noonewould ver...."Agame f he ort escribedandemonstrate,ithrespectoa proposition,hat ts ruth oesnotfollowromny impleuniversalbservationr ntuitiveunch.hepropositionay, f ourse,








still etrue; ut f he easoningnd the videnceanbediscredited,tmust e abandonednless ewgroundsor tcanbefound.

Takespecificallyhefollowinguestion:f n a game iketheone

describedere, hichnvolvesgreat ealof gnorancenthepart feachplayerbout he ther's alue ystem,r evenn onethatnvolves(as the pecificormfthegamedescribedbove oesnot) gnoranceabout ome fthemovesvailableothe ther layerr themoves ehas lready ade, proposalsmade o mprovehe layers'nowledgeabout ach ther'salue ystems,ovesvailable,ositionseached,tc.,whatdoweanticipatebout he dvantagesnddisadvantagesothetwoplayersA propositionrequentlyxpresseds "Itstands oreasonthat heplayero whomwegive hegreaternowledgebouthisop-ponenteceiveshe dvantage."fcourse,na game fthis ort,othplayersanbeadvantagedrdisadvantagedimultaneously,tbeingnon-zero-sumame; his ointedut, he ropositionay erephrasedto the ffecthat he reaterain, rthe elativedvantage,sbound ogo (otherhingseingqual) tothe newhogets hegreaternforma-tion. hispropositionsbased nfaultyeasoning,ut tseems om-patible ithntelligencend ophistication.f t sfalse,s sconjecturedhere,tsfalsityanbedemonstratedya game s simplendartificialas theoneproposed.hosewhoholdtoa propositionfthis ort relikelyohold tonthebasis fvery eneralonsiderations-considera-tions ogenerals tobe contradictedfthepropositionrovedobestrikinglyalsenregardoa simpleittle ame hat,imples it s, sascomplexs the heoreticalodel hatwas mplicitlynmindwhenthepropositionasvoiced.

Thisexamplellustratesnotherspect fthemethodologynvolvedin a game ike his ne.When game implenoughobeanalyzableproduces resultontraryoexpectation,t s likelyoproducetforreasonshat ecomepparentnce he henomenonsobserved,articu-larlywhent sobservednrelationothe tructurefthegame rtoalternativetructuresfthegame. husa conclusionhatsreachedsnotnecessarilyupportedolely ystatisticalvidencerom epeatedplay f gamewhose elevanceotheworlds nquestion.atherhe

conclusion,nce thasbeen uggestedythe xperimentalesults,anoftenerationalizedntheoreticalerms.hegame sthus tangiblerepresentationf theoreticalodel, modelwhosemovingartsanbebetternderstoodftheyanbearticulatedxperimentally.

Thispoint anbeexpressednanotheray. xperimentalames anbeused odiscover,nddemonstrate,mportantossibilitieshatmighthavebeenmissedwithoutt.The significancendrelevancefthese








possibilitiesay till epend n reasoningndon evidencebtainedelsewhere;ut he xistencef he ossibilities,nd ome otionfhowthey elate othe tructurefthegame, anbediscoveredy he rtifi-

cialgame. hiswould, or xample,e true fthepropositionhat headvantagemaywellgo notto theplayerwhoenjoys he ncreasedknowledgend nformationuttotheother layer,ndthat tmayeven e anabsoluteisadvantageooneof theplayersoobtain ewinformationfhecannotonceal hefact hathe has it. (Thispointabout nformationsnotbeing mphasizedere s themain netobeinvestigated,ut s areadilyomprehensiblellustrationf nhypothesistowhichhe xperimentalamewould erelevant.)

On thewhole,t sexpectedhat onclusionseachedythis ind fexperimentalesearch ill notdependmuchon refinedtatisticalanalysis. eshall e ookingor athertrikingesults.ince he ntentistorelatehe bservedhenomenaosome heoryhat losely arallelsthegame tself,s well as to demonstratehepotentialignificance(rather han he actual ignificancen a particularontext) f thevariablesobe manipulatednd observed,maineffort illbe tolearn owtomanipulateheparametersndstructuraleaturesf thegamenordereliberatelyogeneratearticularesultsndphenomena.The ntentsnot,herefore,opursueothe nd prearrangedcheduleforvaryingheparameters,nd subsequentlyo analyze heresultsstatistically.nsteadhere illbefairlyontinualeedbacketweenheresultsbservedndthe urtheresignfthe xperiments.he resultsof thequestionnairexperimentseferredo above llustrate,n asimplecale, hismethodology.

There s a secondaryurposefthis xperimentationhat elatesothedevelopmentftheory.t has todo with hevalueofthesheerconstructionfthe ame ndanalysisf ts tructurendmanipulationof tsparameters.o build game fthis ort,ndespeciallyobuildinto hegame articulareatureshat newishes orepresent,equiresthat nedefineisconceptsperationally.game fthis ortmposesdisciplinentheoreticalodel-building;t can be a test fwhetherconceptsndpropositionsremeaningful,nda means fdemonstrat-

ingsowhen hey re. n the ctual onstructionfthegame, nd indiscussionfthegame's eaturesith ersons hohaveplayedtorobservedtplayed,t hasfrequentlyeen he ase hat ertainlausibleconceptsadtobe abandoned hen nefforto dentifyhemor toincorporatehem) nthegame evealedhat hey eremeaninglessrinnocuous,rthatheyestedn nessentialistinctions.

Closelyelatedstheuseofthegame sa means ftheoreticalom-








munication.f onewisheso definearefully,nd to llustrate,parti-cular istinctionrpropositionbout he trategyfconflict,hegameoften rovides tangiblend unambiguousepresentationfthe on-

cepts nvolved-away of pointingo whatonemeans nd avoidingreliancen ambiguouserbal escription.Two examples ay elp.Onehas odo with henotion f qualityr

symmetrynthe utcomefa game.Asmentionedbove, hepolicy-orientediteraturen imited arfrequentlyseswords ike equality"and"symmetry"nd "reciprocity"n describinghekinds frules ndlimitsroutcomeshatmaybeacceptableo thepartiesnvolved;hetheoreticaliteraturen bargainingnd game trategyoes he ame.'

Andwith n exceedinglynambiguousodel r"game" n mind, ithperfectnformationbout alue ystemsnd themoves nd strategiesavailable, onceptsike "equality"nd "symmetry"an at leastbemeaningfullyefined.uppose, owever,hat ne enricheshegame,even o the imitedxtentf thegamedescribed-oruppose hat negoesfarthertill o add contextualetailwhich,houghnessentialothe ogicaltructuref he ame,ontainsome ower f uggestion,rmoral, asuistic, r legalistic ignificance,r whichentails omeprec-

edent,tradition,r analogy.Then such concepts s "equality" nd"symmetry"-inhe strategiesmployed,n therules and constraintsthat heplayers enerate nd observe,rintheoutcome fthegame-areembarrassedythe heerack of anobviouslymeaningfulefinition.The empiricalontents f theoriginal ropositionhereforeisappear.One cannotdefine equality" n terms f theacceptabilityf an out-come or a ruletobothplayers,nd simultaneouslyreserve nyem-pirical ontentn thepropositionhat ules r outcomeswill be accept-ableonly ftheymeet he onditionf "equality."

The second xample oncernshe tructurefconflicthatsbuiltntothegame. t is interestingo arguewhether hegame described,r avariant f it,captures he spirit f the conflictnvolved n war,racerelations,ndustrialisputes,nteragencyisputes,ureaucraticivalry,or competitionn trafficor heright fway. f one doubtswhetherparticular ame embodies heessentials f a particular ispute,t is

5Closely elated s the dea thatboth idesmust ccept he "same" imits-a proposi-tion hatnotonlymayprove alse n actualplaybutcanprovemeaningless ithin hestructuref the gameunless the game itself s designedwith a symmetricalovestructurend scoring ystem.ee,for xample, ames . King,Jr., NuclearPlenty ndLimitedWar," ForeignAflairs,xxxv (January957), pp. 238-56. For the symmetrynotion n bargaining heory, ee, forexample,JohnHarsanyi, Approaches o theBargaining roblemBefore nd After he Theory of Games," Econometrica,xiv(April 956), pp. I44-57; R. DuncanLuce and HowardRaiffa, ames and Decisions,New York, 957, pp. II4ff.; and T. C. Schelling, For the Abandonmentf Symmetryin Game Theory," eview of Economics and Statistics, LI (August 959), pp. 213-44.








interestingo seewhetherhegame anbe made orepresenthat is-putebyvaryinghe coringystem,he nformationtructure,r thetimingndnaturefthemoves;f tcannot,t s nterestinghen o see

whetheradical hangesn,or additionso,themoves nd scoringsystemanreproducehe ssentialsfthedisputenquestion.n thetrial laysheldso far, t has frequentlyeenthe casethatduringpostmortemplayer enied he nalogy etweenhegame ndthekindofconflictnvolvedn internationalisputes; revisionn thescoringystemasattemptedoreflectomeone'sotion f whatwasessentialoan nternationalispute.t s nterestinghat nmanyasestherevisionhatwould atisfyparticularnalystouldbe demon-

stratedobea non-essentialhange-achange nlyncertainaram-eters,ndnot nthe tructurefthegame. n other ases t becameclear hat ertainypesfdispute ere nherentlyncapablefbeingrepresented.utclarityndagreementouldbe reachedmuchmorequicklyn these heoreticaloints yworking ith he ctual amethanfnotangible odel adbeen resent.

IV. RESEARCH TO BE UNDERTAKEN

A general iscussionf questions orthnvestigatingith gameofthis ort as lreadyeen ublished.6hepresentection illrepeatsomeofthosedeas, upplementhem,ndrelate hem o researchprocedure.

There rethreemain lementsodescribe.he firststhegame, herules ndconstraintsnderwhich twillbe played,hebackgroundagainst hichtwillbeplayed,heparticularlayers howillplay t,and oforth.hesecond oncernshatwillbe

observed-theutcomeof he ame,hebehaviorf he layers,he ecordsept y he layers,particularituationshat evelopnthecourse fplay, nd so forth.Third rethe uestionsrhypotheseshat uide he nquiry,owardwhich hemanipulationfthegameand theobservationfgamephenomenareoriented.o illustrate:necan have hegameplayedwith ifferentules fcommunication;ne anobservehe utcomenterms,ay, fthe woplayers'cores;ndonecangeneralizebout he

value fcommunicationr ts bsence o theparticipantsn a bargain-ingprocess.

( ) THE GAME TO BE PLAYED

Underhefirsteading--theay hegamewillbeplayed rused-the ollowingrrangementsre ontemplated.irst, standardersion

6Cf. Schelling,The Strategy f Conflict, p. 259-63.








ofthegamewillbe usedwith largenumberfplayersostudyherelationfoutcomesomodes fplay,foutcomeso heplayers'nter-pretationsftheir wn and eachother'smodes fplay, ndwhether

there ends o becontinuityrdiscontinuityn thefrequencyistribu-tion foutcomes.orthis urpose,fcourse, theoreticalrameworkfor he lassificationndanalysisfoutcomes,trategiesrmodes fplay, ndplayers'nterpretationsust edeveloped.hiscanbedoneonlynthe oursef he rojecttself,incetrequiresctual lay.

Second,ertaineaturesrparametersf he amewillbevaried.hecommunicationtructureas lready eenmentioned;he nformationstructureinformationf eachplayerbout heother's alue ystem,etc.)willbevaried;he uggestiveetailsfthegamewillbevaried-thescenario,he ctualmap, heprecedentshat anbe createdndbroughtobear,heanguageescribinghe ame nd ts urpose,intsaboutymmetry,ints bout ignaling,tc.; he uantitativeeaturesfthe amewill evaried-thextentfpotentialonflicteneratedy hescoringystem,hepotencyfthe reprisal" ovesvailable,heratioofresourcesvailableothe wo ides,tc.

Third,he rrangementfplays fthegamewill ncludechedulesofrepeatedlaywithinelf-containedroups,lay etween embersfdifferentroupshathavealreadyxperiencedxtendedntra-groupplay,playthat airs xperiencedith xperiencedlayers,nexperi-encedwith nexperienced,ndexperiencedith nexperienced;laythat nvolveseams; lay hatsunder he nfluencefa "mediator"whocanmakecertain inds fproposalso theplayers; laywiththree rmore layersnwhich oalitionehaviorecomesossible;nd

possiblyome laywith he trategyrescribedor neoftheplayers.(2) PHENOMENA TO BE OBSERVED

A meaningfulchemeor ecordinghe utcomesfgamesmust edevised.or a standardersionfthegame,his anbedone ntermsof ndividualet coresndgross coresgross coreshowing rossgainsand gross osses).For comparingheoutcomesf differentvariantsfthegame, meanshastobe devised o "normalize"he

scores; his snot n easymatterecause heres no straightforwardway, or xample,fmeasuringhat player asgotrelativeowhatheshould avebeen xpectedoget nthe oursefplay. Sinceonepurposefvaryinghegametselfstodiscoverhat ifferenceoingsomakes nthe utcome,ecannotely n a priorixpectationsbout"reasonable"cores elativeo whichthe actualscoresmightbenormalized.)








A schemeforclassifyingheplayers' nterpretationsf what theyare about also has to be set up initiallyn connectionwith actualplay-thatis,to someextent y trial nd error.t mustfurthermore

recognize hattheplayers' erceptionf thegame,and theirmodeofplay, anundoubtedlye affectedythe nstructionshey regiven,the questionnaireshey re askedtomaintain,nd the notesthey reaskedtotakeon their wn strategiesron their artners' lay. Howquickly playerbecomes lert o thepossibilitiesf signalingn thegame sundoubtedlyffectedywhether e has been nstructedolookfor ignals ndtorecord isown.His actualperceptionfsignals ndchoice fmethodsfsignalingwill ikely e affectedfparticularypesof signals hathe is to look for are specifiedn theinstructions.)ngeneral, he player's elf-consciousnesss likelyto be stimulated yanyexplicit nalytical rameworkn whichhe is asked to recordhisintentionst eachmove, he ntentions e imputes o hispartner,ndtheunderstandingse thinks hetwo of themhave reached.Neverthe-lessrecords f this ortwill be an essential artoftheresearch,incean importanturpose s to study hedevelopmentf understandingsand misunderstandings,heprocessof inventinganguageforcom-municatingroposals, he dentificationf critical turning oints" nthe course fa game,therelation f each player's xpectationso thesuggestive etailsbuilt ntothegame,the correctnessf players' on-jecturesboutmissingnformation,nd eachplayer's asicconceptionofstrategy,uchas the claimshe insists n and theriskshe is willingto take. How manyof these ttributesf thecourseof thegame,asperceivedy a player, an be defined perationallynd put ntoa log

orquestionnaireithout isruptinghegame toomuchremains obeseen; talsoremains o be seen bytrial nd errorwhichamongtheserecords roducedata thatpromise o be interesting.

The analyticalategories orobservingndrecordingmodesofplaywillalsohavetobeworked ut nactual bservationfplay. Co-opera-tive"vs. "uncooperative,"bold"vs. "cautious," aggressive"s. "fairand reasonable,"self-oriented"s. "partner-oriented,"nd otherdis-tinctions ayormaynotproveusefulnpracticendareundoubtedly

inadequate.t remains o be seen,too,whether player, is partner,andtheobserverhare imilar erceptionsboutthemode ofplay, ndthe intentionsehindit. The alertness f a playerto his partner'sproposals, is relianceon collaboratingn searchof a language,hisinterestnexploring isopponent's aluesystem,isconception ftheproper se ofstubbornnessrpunishment,isrefusal ocommunicate,orhispretenset notunderstandingispartner,s wellas variousmore








"topological"spectsfthemoves emakes,mayprove obemean-ingfulategoriesor nalysis.

(3) LINES OF INQUIRYA particularhenomenonobe investigateds thedevelopmentf

language,ules,ndtraditionsnan nbredroup fplayers.epeatedtwo-personlay na random rround-robinasis mong,ay, our osixplayershould roviden interestingpportunityor tudyingheinventionf anguagehroughhemedium fmoves fthegame, ndthedevelopmentfrules nd limits fconflicthat regovernedysheer orce ftraditionnd expectation.he extent owhich hese

processesan beretardedrstimulatedy dding uggestiveaterialsto thegame;howthe nventionfsignals nteractsith nyactualovert ommunicationhat s permitted;owrapidlyignals rrulesareconvergedn nthe oursefrepeatedlay; he orrelationmongthe ignalsndrules hat evelopndifferentnbred roups;ndthequestion fwhathappenswhenpairs redrawn rom wodifferentinbred roups-all hesewillbe part fthestudy.Here it will beparticularlyifficultogetplayersoexpresshemselvesnresponseointerviewsndquestionnairesithoutontaminatinghe rocesstself.)

A specificeaturefthegame o beinvestigatedsthedeterminantsof"instability."y"instability"smeant ere he endencyfa gametogeneratemutuallyestructiveehaviornd low scores. he trialplays fthepresentariantuggesthattmay edifficult,t east orcertaininds fplayers,oget hemutofa cautiousndco-operativeframe fmind ndtocreateomethingnalogouso"war" robserva-bleconflict.

xperimentuggestshatmore onflictanbe generatedby earranginghe aluesf tatesnthemap.t seems orthonjectur-ingthat he reprisal" ove ontained ithinhegame, ra changein themoveshat ives strongdvantageo theplayerwhobreaksanagreementengagesn"surprisettack,"or xample),may reateinstability.heresalsoevidencehat he empofthegame,smeas-uredbythenumber fmoves hat anbemade t eachturn,rthepaceatwhich ieces an beadvancedver heboard,ffectstability.

Andthere s reason o conjectureplusa bitofsuggestivevidencefromhetrial lays)that hedistributionfoutcomes aybequitediscontinuousith espectocontinuousariationfcertainarame-ters-i.e.,hat strikinglyimodal istributionfscoresmainly uetothe egreef"destruction"fvalue)occurs ith espectovariationinoneofthese eatures.

Theresnofixedchedulefplaysndvariationsobepursued.here








is rathern arrayf mportantndfascinatinguestionshat hegamemay elp opursuer maynot.As indicatedarlier,hegeneralnten-tions to dentifyhemost trikingesults,o pursuehose uestions

to which hemostnterestingnswerseem o be emerging,ndtomanipulatehegame o generatenterestinghenomena,articularlythosehat ontradictffhandxpectation.he initialxperimentationwill hereforeave o be exploratory.nanycase, gooddealof trialand error illbe involvednworkingutthe nalyticalramework.Inother ords,he bject snot otest set favailableypotheses,omuch s to generateypotheseshroughxploratoryxperimentation,to manipulatehegame nd ts nvironmentnan effortobringhesuggestedypothesesnto learerelief,ndtorationalizeheresultsintermsf theoreticalodelhat anbe dentifiedithinhe tructureofthe ame.7

7A recent, airly omprehensiveescriptionnd discussionf ess formalizedpoliti-cal games" hat nvolve gooddeal of free ctivitys in Herbert oldhamer ndHansSpeier, SomeObservationsn PoliticalGaming,"WorldPolitics, ii (October 959),PP. 7i-83.A muchmoretightlyormalizedamestructureas been usedbyHaroldGuetzkow and describednpapers resentedo conferencestNorthwesternniversity

in April I959 and West Point in June i959). An extensivehistoryof war gaming,especiallyn thenineteenthenturyndup to WorldWar II (butwith omediscussionofmorerecent ames), s in John . Young,A Survey fHistorical evelopmentsnWarGames,Washington,.C., Operations esearch ffice, ohns opkinsUniversity,March 959; another ather omprehensiveiscussions in ClaytonJ.Thomas andWalter . Deemer, The RoleofOperational aming n Operations esearch," pera-tionsResearch,v (February I957), PP. I-27.

A discussionf whatwargaming an and cannotdo is in RobertD. Specht,WarGames,The RAND Corporation, aper P-IO4I, I957. For a discussion f whetherexperimentalameshave, n principle, esearch alidityn the senseof producingempirical vidence, ee Herman Kahn and IrwinMann,War Gaming,The RAND

Corporation,aperP-ii67. (The present roposal,nd thequestionnairexperimentsreportedn the earlier rticle,re at variancewith theviewexpressed yKahn andMann.)

Someformalizedne-movend two-moveames, n some cases teratedhroughseries f plays, re reportedn MortonDeutsch, Trustand Suspicion," ournal fConflictResolution, i (December958), Pp.265-79;inMerrillM. Flood,"SomeExperi-mentalGames,"Managementcience, (October 958), pp.5-26; n Bernhardtieber-man, "HumanBehavior n a Strictly etermined x 3 MatrixGame," BehavioralScience, (October960), PP. I7-22; inJ. ayerMinas,Alvin codel, hilburn atoosh,andMiltonLipetz, SomeDescriptive spects fTwo-Person on-Zero-Sum ames,"Journal fConflictResolution, II (June 959), pp. II4-I9; and in RichardH. Willis nd

Myron . Joseph,Bargaining ehavior,"bid.,pp. 02-I3.Business ames,which have come into vogue as training evices nd as researchtools, re usuallynearer in formalization) o the present ame than the politicalgames described y Goldhamer nd Speier, are a degree more formal than theGuetzkowgames, nd are more like the older,highly tylizedwar games of thenineteenthentury han ike the war gamingpresentlyracticed. or a buying-and-selling ame thatwas designed or nd extensivelysedin research,ee Sidney iegelandLawrence . Fouraker, argaining nd GroupDecisionMaking,New York, 960.

The game that omes losestn spirit o the one describedn the present aper sprobably he "balanceof power" game described n MortonA. Kaplan, Arthur ee








4ppendix

INSTRUCTIONS FOR THE GAME

Takingpart nthis tudy resentsouwith heopportunityfearningfrom minimumfthree ollars o a maximumf seven o tendollars.Thisgame s not ike hess,heckers,rmonopoly,herewhat neplayergainshisopponentoses.n thisgame tis oftenhecasethat ertainut-comeswillbe betterorboth layershanother utcomes.omemannerofplaymaymaximizehe mountachplayeranearn.But, t the ametime,nthegame here illprobablyevalues statesworthmoney)whichboth ou ndthe ther layer illwant. hus, he ituations one n whichthere s someelementf conflict;ut also someelement f "commoninterest"r "commonain" s present.he purpose f playinghe gameisnot odefeathe therlayer ut o earn smuchmoneyspossible.

The game snotnecessarilyfair" n the ense hat ftheplayersrriveatwhat ppearso bean equaldivisionf the tates,heywilleachearn nequal mountfmoney.henumberf oloredtatesmay e quite ifferentfor achplayer,ndthe arrangementfthecolored tates n theirmapsmay end oproducenequal arnings.t is alsopossiblehat n apparentlyunequaldivisionfthe statesmayyield arningshat re approximatelyequal.

Thegame nvolves map, setof chips, scoringystem,nda setofrules boutmoves. he playersmove n turn: t eachturn player anplace number f chips nthemap andremove number. t the ndofthegame player'sarningsepend ntheconfigurationf hischips nthemap, nd on the losses" e hassufferednthe ourse f play.

TheMapThemap s an ordinaryutlinemapof the48 states fthe continental

United tates. he 48statesretheunitsntowhich hemap s divided.

Player's arnings

A player'sarningsepend n thevalues f the tates epossessesttheendofthegame, lusthechipshe possesses, inus he"damage" onetohim.

StateValues nd Their ossession: he Integral rea

The values fmany fthe tates ifferor he woplayers.achplayer

knows hevalues fall the states o himselfut not their alues o theother layer.Eachplayer asa numberfcolored tatesredorblue) whichhavea

Burns, nd RichardE. Quandt,"TheoreticalAnalysis f the 'Balanceof Power,'"Behavioral cience,v (July 960), pp. 240-52. While it is oriented owarddifferentbargaininghenomenahan hepresentame, ts rationalendmethodologyremuchthe same,especiallyn theauthors'nterestn using t both as a "game"and as a"theoretical odel."








premiumvalue; they re worth50?. The remaining tates re whiteandareworth 0 each.These valuesare what the states re worth o theplayersifhepossessesthem t theendofthegame.

The colored tates rechosenbya randomprocess nd so there s no wayofdetermining,t theverybeginning f thegame, the colored tates f theother layer.tispossible hat ne ormore tatesmaybe colored edandblue.

The play ofthegame usestwomaps separated ya barrier. ach playerhas before ima map,withhis own statevalue-systemully bservable ohim, uthe snot ble tosee theother layer'state alues.Each playermakeshisown moves ndalsoreproducesheother layer'smoves nhismap.Thusall moves revisible obothplayers, uteachother's tatevalues arenot.

A state s possessed y a player, t theend ofthegame, f t is partof anintegral rea thathe occupies.

A player'sntegralreaconsists f a set ofstateswhich reoccupied olelybyhis chips, r boundedby stateswhich are occupiedsolelybyhis chips.The area must ontain heplayer's ome base and mustnotalso containhisopponent's ome base.The states n itmustbe geographicallyonnected oeachother ndmustform distinctrea.Each statewithin hearea neednotbe occupiedbytheplayer's hipsbut a boundarymustexist.This boundarymustconsist f states ccupied olelybytheplayer's hips, xceptthat theborder ftheUnitedStatesmay be usedto form he boundsof the ntegralarea. States

within hebounds of an integral rea need notbe occupiedtobe possessed.Anotherway ofdefining n integral rea is to saythat t is an area (set

ofstates),ncluding heplayer's omebase,whichthesecondplayer annotenterfromhis own home base withoutmovingthrough state (placingchipson it) whichthe first layeroccupies olely, r by goingoutsidetheborder ftheUnitedStates.

At theend ofthegame, fbothplayers avechipson a state, either anpossess hestate, orarethechips ost.The statevaluespossessed y a playerat the end of

thegame consist f thesumof thevalues of the states on-tained n the area he possesses,ncludingthe boundary tates, ccordingtohisown schedule fstatevaluesas indicated n his own map. The statevalueson the econdplayer'smapdo notaffecthefirst layer's core.

During the courseof play the first wo integral reas formedby eachplayerwillbe announced.

Home base, specifiedtate or achplayer,smarked nbothmapsand isknown o bothplayers. player lwaysoccupies rpossesses ishomebase,whether r not he places any chips on it. A playercan neverpossess or

occupy hesecondplayer'shome base.Chipsand TheirUse

Red,blue,black,and whitechipswill be used in thegame.One player,knownas "Red," makes his moveswith red and black chips; the other,known s "Blue,"makeshismoveswithblue and white hips.

A chipplacedon a state an do one ofthefollowinghings: t can occupysolely, ccupyointly,hallenge, r fight.








When a playerplacesone,ormore, f his red (or blue) chipson a statehe occupies t. He occupies t solely fthe secondplayerdoes notplace (orhas not alreadyplaced) his blue (or red) chips on the state.A state soccupiedointlyfbothred and blue

chipsare

placedon it and it is not

atchallenge.When a playerplacesone of his black (or white) challenge hipson a

state, hat tate s then t challenge. hallenges an be made whether r notthesecondplayerhas chipson the same state, nd even if there s no redorbluechipon a state.A playermaymakeas manychallenges s he wishesand withdraw s many s he wisheson eachplay,butonlytheplayerwhomade a particularhallengemaywithdrawt.Onlyone challenge hipmaybe on a state t any time.

If oneplayerhas chipson a state nd the secondplaceschipson thesamestateand challenges,he firstmustwithdraw r fight.He withdraws y

removing ischipsfrom hat tate t hisnextturn.He fights yindicatingso at his nextturn, nd bothplayers' hips are removed rom he state nequal numbers o thatonlytheexcessnumberof chips (if any) that oneplayerhad remains n thestate.The chips o removed re ost. At the endofthegame lostchipsdo notcontributeo a player's arnings.)

If a playerresponds o a challenge n a particulartateby"fighting" orit, and placesmorechipson itthantheother layerhas there, o thatuponremoval fequal numbers e has

someremaining, is remaining hipsareautomaticallyt challenge t thenext urn. The fight,n effect,s stillon.)The playerwhofirsthallengedmayadd chipsat his turn, emoving qualnumbers gain,and so on until, orone turn, ne player dds no chipstothedisputed tate.At thatpoint fightings over"on that tate;theremain-ing chips,once one playerhas playeda turnwithout ontinuinghefight,are at challenge nlessthechallenge hipis removed.

If a playerplaceschipson a statethathas no chipsof theotherplayer,and challenges,heother layer annot ubsequentlylace chipsofhis ownon the statewithout utomatically ighting,.e., without

removing qualnumbers f chips forbothplayers o thatonly theexcessof chipsof oneplayer emains.One mayfightwith greater umber fchips, hushavingchipson thestate fter emoval;one mayfightwithan equal numberofchips, o that ll chips reremoved rom hestate;orone mayfightwithalesser umber fchips, o that hechallengeretainsomechipson thestate.)

It canhappenduring hecourse f a dispute or state hatneither ronlyone playerhas colored hips red orblue) on a state. n these asesneitherplayer olely ccupies he tate nless heother layer ashad an opportunity

to make a move (i.e.,place one of his redor blue chips on thestate) andhas notplacedchipson thedisputed tate.Once a playerhas formedn integral rea,thesecondplayer annotplace

a chipwithin heboundaryfthat rea.To placea chipwithin heboundary,he must first break"theboundary f theintegral rea by placingone ormore of his red (or blue) chipson a boundary tate or states,f this snecessary). This mayormaynot result n fighting,epending n whethertheboundary tates re at challenge.)








Cutting fgAt anytimeduring hegame that one playerpossesses n integral rea,

anychipsof the secondplayerwithin he area boundedmaybe (but need

notbe) removed ythefirst.fthey reremoved,hey re osttotheir wner.Chips ost n thisfashion re referredo as "cutoff."Note that chipmaybecome utoff,ftheplayer uttingt off ompletes boundary yplacingchipson unclaimed tates, r ifhe accepts challenge nd fights,hefightendingwith his possession f the state. f he has to challengeor fight norder o achieve oleoccupancy f a stateformingheboundary,hesecondplayermay,at his turn, emove hechipsthatare in dangerof beingcutoff. The number hatmaybe removed s subject o the over-all imit onnumber emovable t a turn,mentioned elow.) In addition, he integral

area s notcompleted ntil hefight or hestate s completed,.e.,untiltheplayerwhogivesup thestatehas had an opportunityo place one or morechipson thestate ndhas declined heopportunity.

If, after he game is terminated, player'schips are withinthe otherplayer'sntegral rea,thesechipsare not cut off.They are removedfromthe boardand returned o their wner.

Home-BaseDamage

A chipmay be usedto inflictamageon theother layer. his is doneby

placing t on his homebase. If that s done,thechip is removed nd losttotheplayerwhosechip t s,buttheplayerwhosehomebasewas so affectedloses n amount fmoney quivalent othevalueoffive hips 250). A chipon a homebasehas only hisresult nd doesnot"claim"anything.

Play

The playof thegame consists f a seriesofmoves.A move consists fremoving ndplacingone ormorechipson one ormore tates.Who makesthefirstmove sdecidedbyflipping coin.Ateachturn, playermayremove

anynumber p tofiveofhis own chipsfrom tates heywere on and mayplaceany numberup to fiveof his chips on states.He need notmove anychips;this s doneby ndicating "pass." (Chips removed,xceptwhen ostbyfightingr cut off, re available to be placed again on the map, andmay be so used at the same turn, ubjectto the limit of five n the totalnumber hatmaybe placedon states t a turn.)

A playermaymakeas manychallenges s he wishes t a turn, nd with-draw as manychallenges s he wishes.

There sno limit ohowmany hips playermayplace, at a turn, n theother's omebase (except, fcourse, hatnomore hanfivemay be removed

from tatesforthatpurpose at a turn in the eventnone are otherwiseavailable).

Each playerhas 50 red and 50 blue chips. (Red's blue chipsare used toreproduce lue'smoves on Red's map,and viceversa.)

The game is terminated hen one player a) makes no move and (b)makes an offer o terminate,nd theotherplayer ccepts heoffer,making








no move. f the offers not accepted, heplayermakingtheoffermaynotthenmoveuntilhis nextturn.

At termination,fany statecontains hipsofbothplayers and is not atchallenge),the chipsare removedfromthesestates nd returned o eachplayer.Neitherplayer ccupiesor possesses he state.

The amounteach player arnsdependson the chipshe has remaining(either n states rnoton states), hevaluesofthe tates epossesses,ndthedamagehe has suffered. player's arnings renotdependent n the otherplayer's arnings.It is absolute arnings, otrelative arnings, hatmatter.)

No communicationetweenplayers s permitted.ach playerwriteshismove on a card and makesthemove on his own map. The Experimenterthenexecutes he moveon the secondplayer'smap. He removes ll chipsthat re lostthrough ightingr cutoff.

Some Arbitrary eographicalRules

Wherefour tatesmeet n a corner,n thesouthwest, diagonalpairdoesnot close a boundary i.e.,New Mexico,Utah, and Idaho do not form aboundaryaround the West Coast; New Mexico, Colorado, Utah, andIdaho do).

Upperand LowerMichigan, lusLake Michigan, re considered singlestate;thus llinois nd Indianabothborder n Michigan nd do notborderon Canada. Ohio borders n Canada; so doesPennsylvania.

1961 Experimental Games and Bargaining Theory

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Transcript of 1961 Experimental Games and Bargaining Theory