IEEE TRANSACTIONS ON COMPUTATIONAL SOCIAL SYSTEMS 1...

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IEEE TRANSACTIONS ON COMPUTATIONAL SOCIAL SYSTEMS 1

A Signaling Game for Uncertain Data Deliveryin Selfish Mobile Social Networks

Feng Xia, Senior Member, IEEE, Behrouz Jedari, Laurence Tianruo Yang, Jianhua Ma, and Runhe Huang

Abstract— Cooperative data delivery among mobile nodes canimprove the performance of data delivery in mobile socialnetworks. However, data routing in the presence of sociallyselfish (SS) nodes is challenging, where they mitigate the degreeof their cooperation level based on their social features andties to achieve their social objectives. This issue becomes morechallenging when they prevent revealing their reactions aboutincoming messages, which leads data forwarding under uncertainbehavior. In this paper, we propose a signaling game approach,namely, Sig4UDD, to study the impact of uncertain cooperationamong well-behaved and SS nodes on the performance of dataforwarding. In Sig4UDD, we employ Bayesian Nash equilibriumto analyze one-stage interactions among nodes. Then, perfectBayesian equilibrium is applied to analyze their multistage inter-actions. In this stage, we establish a belief system to help SS nodespredict the type of their opponents and take appropriate actionsto maximize their utilities. To update the beliefs of SS nodes,we devised the weighted social distance metric to measure theglobal social distance among nodes. Finally, we compare theperformance of Sig4UDD to some benchmark cooperative andnoncooperative data forwarding protocols using Reality Miningand Social Evolution data sets.

Index Terms— Mobile social networks (MSNs), node selfish-ness, opportunistic data routing, signaling game.

I. INTRODUCTION

MOBILE social networks (MSNs) [1] are the emergingparadigm of communication in environments, where

end-to-end connectivity between mobile nodes (i.e., devicesand users) may not exist due to their rapid movement. Hence,delay-tolerant networks (DTNs) [2] are employed as coretechnologies to establish data routing among nodes in anopportunistic manner where the nodes contact each otherthrough wireless technologies such as Bluetooth and Wi-Fi.Recently, the characteristics of cyber-physical systems andsocial networks (called cyber-physical-social systems) havebeen integrated to improve the quality of services in MSNs.In MSNs, the social features of nodes are exploited to predicttheir future contacts and improve the routing performance.

Manuscript received July 12, 2015; revised March 10, 2016 andMay 25, 2016; accepted June 8, 2016. This work was supported in partby the Fundamental Research Funds for the Central Universities underGrant DUT15YQ112 and in part by the National Natural Science Foundationof China under Grant 61572106.

F. Xia and B. Jedari are with the School of Software, Dalian Universityof Technology, Dalian 116620, China (e-mail: [email protected];[email protected]).

L. T. Yang is with the Department of Computer Science, St. Francis XavierUniversity, Antigonish, NS B0H 1X0, Canada (e-mail: [email protected]).

J. Ma and R. Huang are with the Faculty of Computer and Information Sci-ences, Hosei University, Tokyo 184-8584, Japan (e-mail: [email protected];[email protected]).

Digital Object Identifier 10.1109/TCSS.2016.2584103

Fig. 1. Sig4UDD addresses SS data forwarding under uncertain nodecooperation.

The motivation is that the nodes’ social features have long-term characteristics that provide reliable connectivity amongthem [3].

A key assumption in most existing MSN routing protocols(such as SimBet [4], Bubble Rap [5], and PIS [6]) is thatnodes are fully cooperative (FC) and they willingly relaymessages for other nodes to increase network utility. However,some users may not always cooperate in data relaying due tovarious reasons (such as resource limitations, privacy concerns,or social objectives) and exhibit selfish behavior. In general,two types of selfish nodes can be defined [7]: individuallyselfish (IS) nodes and socially selfish (SS) nodes. IS nodesrefuse to relay incoming messages without considering theirsocial relationships while they aim to increase their individualutility by forwarding their own messages. In contrast, SS nodesmitigate their cooperation degree based on their social tiestrength to maximize their social utility.

Fig. 1 compares the impact of the nodes’ cooperation levelon the routing performance regarding their social awareness.The horizontal axis is depicted from social oblivious to socialawareness, and the vertical axis is drawn from FC to non-cooperative. As shown in this figure, the nodes’ cooperativebehavior increases the network global routing utility, whereasIS behavior maximizes the nodes’ personal profits. However,SS nodes may increase or decrease their own utility and thenetwork utility due to their conflicting interests and benefitsin messages.

A major challenge about the SS node behavior is identifyingtheir cooperation (or willingness) degree. To deal with thisproblem, Li et al. [7] assume that users determine theircooperation level with others through the interface of their

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2 IEEE TRANSACTIONS ON COMPUTATIONAL SOCIAL SYSTEMS

device manually. In [8], contact history among nodes is usedto identify the cooperation degree of nodes. Nevertheless,we believe that the cooperation level of SS nodes should beidentified based on their realistic social information. Mean-while, SS nodes prefer that their forwarding actions shouldnot be observed by others. Under these circumstances, asender node cannot make sure whether another encounterednode would accept and carry its forwarding messages. Hence,message forwarding is made under uncertainty, which raisestwo important open issues as follows.

1) How to deal with uncertain data delivery in the presenceof SS nodes when they do not reveal their messageforwarding decisions.

2) How the uncertain cooperation among the FC and SSnodes affect the routing performance.

We use a class of dynamic Bayesian game called signalinggame [9] to address the questions mentioned previously. Thesignaling game is a noncooperative game with incompleteinformation, which allows us to formulate different conditions,especially in a competitive network that some informationavailable to a player may not be available for others. In ourscenario, an SS mobile node does not have complete infor-mation on its opponents’ actions. Nevertheless, it can use thenodes’ social features to establish its beliefs and predict theother nodes’ future actions.

In this paper, we propose a signaling game, calledSig4UDD, to model uncertain cooperation among FC and SSmobile nodes where the type of each node cannot be observedby others. We apply Bayesian Nash equilibrium (BNE) toanalyze one-stage communication between the encounterednodes (game players). In this way, we prove that a playerwould gain an optimal payoff, given the strategy of anotherplayer. Then, we use perfect Bayesian equilibrium (PBE) tofind the best response strategies of the players based on theircurrent beliefs. In this stage, we design a belief system tohelp the SS nodes predict the type of their opponents. Thebelief system is updated based on the properties of eachmessage according to Bayes’ theorem. For this purpose, weintroduce the weighted social distance (WSD) metric by givinga novel definition of social similarity to compute the overallsocial distance among the nodes where the importance ofeach feature is associated using a weight factor. Finally, wedemonstrate simulation results to evaluate the performance ofSig4UDD using Reality Mining and Social Evolution datasets.

The major contributions of this paper can be summarizedas follows.

1) We are the first to study uncertain data delivery amongwell-behaved and SS nodes considering their realisticsocial features.

2) We advocate a belief-based game-theoretic model toanalyze one-stage and multistage interactions amongmobile nodes.

3) Our experiments involve two real-world data sets includ-ing the users’ mobility and social information, and theresults let the protocol developers and researchers tomake appropriate decisions about the users’ realisticselfish behavior.

4) The comparison of Sig4UDD with some cooperativeand noncooperation routing protocols illustrates thatSig4UDD outperforms the other algorithms in terms ofmessage delivery ratio with low communication cost.

The rest of this paper is organized as follows. In Section II,the related works are reviewed. In Section III, the networkmodel and assumptions are presented. In Section IV, ourproposed Sig4UDD scheme to address uncertain data deliveryin the MSNs is introduced. In Section V, the evaluation resultsare reported. This paper is concluded in Section VI.

II. RELATED WORK

Most of the existing routing protocols in DTNs, such asEpidemic [10], CAR [11], and PRoPHET [12], use the nodes’contact history to predict their future contacts. Recently,social-based routing protocols have been proposed that usethe nodes’ social characters to further improve the routingperformance (see [13], [14] for surveys). For example, BubbleRap [5] exploits the community structure and node centralityto make forwarding decisions. dLife [15] uses a weightedsocial graph to model time-evolving social ties among mobilenodes. Then, messages are forwarded to the nodes that havestronger social ties with the destination than the current carrier.

Several studies explore the impact of the nodes’ IS behavioron DTN routing protocols [16]–[18]. Based on the simulation-based and analytical methods, the evaluation results reveal thatthe performance of data forwarding is degraded considerablyif the majority of nodes shows IS behavior. For instance, theexperiments in [16] demonstrate that if 100% of nodes areIS, the delivery ratio in the Epidemic routing drops to 40%.Hui et al. [19] conclude that MSNs are robust to differentdistributions of node selfishness due to the nature of multiplepaths. To stimulate selfish nodes to carry data for others,various incentive schemes, such as barter (or Tit-for-Tat) [20],credit-based [21], reputation-based [22], and game-theoreticmethods [23], have been designed in DTNs. However, themajority of existing methods cannot be directly applied to dealwith social selfishness, because they do not consider the nodes’social behavior.

In contrast to the individual selfishness, a few studieshave explored the impact of SS behavior on DTN routing.Li et al. [24] divide network nodes into two communities,where each node only relays data for nodes that belongto the same community. Based on analytical methods, thispaper depicts a boost in data delivery delay and a cutbackin data delivery cost in the presence of SS nodes. Similarly,Give2Get [22] detects packet droppers in the Epidemic routingunder the assumption that nodes are selfish with outsiders(i.e., nodes from other communities). Among other results,it is shown that the selfish node detection probability is morethan 91%.

Closely related to our work, SSAR [7] formulates messageforwarding among SS nodes as a multiple knapsack problem,where intermediate nodes are selected based on their contactopportunity to destination nodes and their willingness level.However, the willingness level of SS nodes in SSAR isidentified once when the user joins the network manually.


XIA et al.: SIGNALING GAME FOR UNCERTAIN DATA DELIVERY IN SELFISH MSNs 3

Fig. 2. Network model in the Sig4UDD scheme.

Furthermore, Sermpezis and Spyropoulos [8] investigate theimpact of social selfishness on DTN communication per-formance when the selfishness level of nodes is identifiedbased on their mobility patterns. In the simulations, therelation between power consumption, message delivery delay,and message delivery probability is investigated using bothsynthetic and real-world mobility traces. Similarly, Wei et al.[25] propose Context-Aware Message Forwarding (CAMF),in which node selfishness is considered as a requirement ofsystems. In CAMF, the selfish characteristics of SS nodes areused to reduce their resource consumption. However, in themajority of the methods mentioned above, the realistic socialinformation of nodes has not been used to identify their socialties and willingness level.

Game-theoretic approaches also have been employed todeal with selfish nodes in DTNs. For example, Mobicent [21]allows the underlying forwarding protocol to select the mostefficient routes between the source and destination nodes.Then, a path auction game is applied to design reason-able costs and reward parameters, which lead to a PBE.In Mobigame [26], a user-centric reputation-based schemeis proposed to stimulate cooperation among cooperative andselfish nodes. To achieve fairness, Mobigame uses a Bayesiangame approach to design reasonable costs and reward para-meters. However, both Mobicent and Mobigame have notconsidered the social features of nodes in their incentivemechanism. Quite recently, Dong et al. [27] introduce quality-of-experience in MSNs and investigate recent advances in thisarea. Then, Dong et al. [28] explain how a game theory candepict social behavior, price competition, and the evolutionaryrelationship among mobile nodes.

III. SYSTEM MODEL AND ASSUMPTIONS

In this section, we present the system model and the nodes’uncertain behavior.

A. Network Model

As shown in Fig. 2, the structure of the network modelin SIg4UDD is considered in two views: the physical networkview and the social network view. In the following, we explainthe properties of each view.

1) Physical Network View: We consider a network com-posed of N mobile nodes in which the nodes do not dependon any infrastructure and contact each other by Bluetooth

interface. Furthermore, periodic node contacts with the accesspoints to Wi-Fi are established to capture the nodes’ socialinformation. The movement patterns of the nodes are basedon their social behavior. In addition, a node can contact onlyone node at a time where the contact includes a contact timeand a contact duration.

2) Social Network View: In this view, the links amongthe nodes are identified based on their social similarities.We model this structure as a sequence of dynamic weightedgraphs G = {G0, G1, . . . , Gt , . . . }, where Gt = (Nt , WSDt )represents a time-dependent network graph at time t. In thisgraph, the vertex set Nt is the set of active nodes andWSDt = {(i, j)|i, j ∈ Nt } is the edge set at time t. In addition,wsdt

i, j = {wsdti, j ∈ [0, 1]| i, j ∈ Nt and (i, j) ∈ Et } denotes

the tie strength between nodes i and j, where wsdti, j = wsdt

j,i .Note that wsdt

i, j = 1 implies that i and j have totally dissimilarsocial features, and hence they do not care about the utility ofeach other. Furthermore, wsdt

i, j = 0 implies that i and j aresocially similar and they care about the utility of each otheras their own utility. We present the calculation of the socialties among nodes in Section IV-B.

B. Message Model

We use a uniform message generation pattern in whicheach node i ∈ N generates its messages to be destined byany other randomly selected nodes. Similar to SSAR [7], weassume that each node has unlimited storage resource to storeits own messages, but they have limited buffer space to storemessages received from other nodes. Mi = {m1, m2, . . . , mk}denotes the list of messages in i’s buffer. A sample message mhas four attributes: source ID (srcm ), destination ID (desm ),feature space of source node (Ft

s ), and message time-to-live (TTL) (ttlm), where srcm and desm are, respectively, theunique identity of source and destination nodes, Ft

s includesthe social features of srcm in time t, and ttlm is the time afterthat m expires.

C. Node Type

An important concept in Sig4UDD is the notion of nodetype that identifies the forwarding behavior of the nodes.We assume that there are two types of nodes in the networkwith the following behavior.

1) FC nodes relay messages on behalf of other nodes eventhough this brings no individual utility for them.

2) SS nodes relay messages received from other nodesbased on their social similarity to maximize their socialutility as well as their individual utility.

IV. OUR PROPOSED Sig4UDD METHOD

A. Sig4UDD Structure

Fig. 3 shows the structure of Sig4UDD that includes threecomponents. In the following, we introduce each componentand explain their modules.

1) Social Feature Management: This component managesthe social features of nodes and measures their tie strength.In this component, we design two modules, Dynamic WeightedGraph that generates a social graph for the network and WSDmodule that identifies the strength of ties between nodes.



Fig. 3. Overall structure of Sig4UDD.

2) Belief System: This module establishes the belief of SSnodes about the type of other nodes that includes two modules,Belief Initialization and Belief Update. The Belief Initializationmodule assigns the prior belief of nodes when they contacteach other for the first time. The Belief Update updates thebelief of nodes based on the properties of messages.

3) Message Handler: This component includes a PriorityManager module that identifies the forwarding priority ofmessages and a Buffer Manager module that manages thebuffer of nodes when it overflows and checks the TTL ofmessages to drop expired messages.

4) Data Delivery System: This component managesthe transmission of messages between encountered nodes.We design three modules in this component. AltruisticSender/Receiver manages message forwarding and receivingfor FC nodes, whereas SS Sender/Receiver handles mes-sage transmission for SS nodes based on their social utility.We design a Socially Utility Estimator module to quantify theutility of each message for an intermediate node.

B. Social Feature Manager

This component includes modules Dynamic WeightedGraph and WSD. The Dynamic Weighted Graph buildsa time-varying social graph over the physical network(see Section III-A). The WSD module identifies the strengthof ties among nodes. The motivation is that exposing socialsimilarity favors cooperation among nodes in dynamic net-works [29]. Although some similarity functions (such asHamming [30] and cosine angular [31]) have been proposed,the existing metrics have not considered the significance ofeach feature, while we believe that the importance of thenodes’ social features can be different. For example, a directcontact between two nodes might be more important than ashort message.

In the WSD metric, we use the Gower coefficient [32] toidentify the social similarity of nodes. We assume that thereare N nodes with K features represented with an N ×K matrix

Ft =

⎡⎢⎢⎢⎣

f t1,1 f t

1,2 · · · f t1,k

f t2,1 f t

2,2 · · · f t2,k

......

......

f tn,1 f t

n,2 . . . f tn,k .

⎤⎥⎥⎥⎦.

Given feature spaces Fts = ( f t

s,1, f ts,2, . . . , f t

s,k) andFt

r = ( f tr,1, f t

r,2, . . . , f tr,k) at time t, we define wsdt

s,r betweentwo nodes s and r as follows:

wsdts,r =

∑Kl=1 δt

s,r(l)Sts,r (l)∑k

l=1 δts,r (l)

(1)

where δts,r(l) = 1 if Sender and Receiver can be compared

with feature l (i.e., the values are not missing); otherwise,δt

s,r(l) = 0. This is because Sender and Receiver only haveaccess to the features of their encountered nodes.

In (1), Sts,r (l) is quantified as

Sts,r (l) =

∣∣wts,l f t

s,l − wtr,l f t

r,l

∣∣max

(f tN,l

) − min(

f tN,l

) (2)

where f ts,l and f t

r,l , respectively, denote the value of feature lof Sender and Receiver. Furthermore, wt

s,l and wtr,l are the

weights of features f ts,l and f t

r,l , respectively, which can takeany value between 0 and 1. Moreover, f t

N,l runs for allnonmissing values of feature l of all N nodes. As a result,the quantity St

s,r (l) can get a value between 0 and 1. In (2),wt

s,l is calculated as [33]

wts,l =

f ts,l∑n

a=1 f ta,l

f ts,1∑n

a=1 f ta,1

+ f ts,2∑n

a=1 f ta,2

+ · · · + f ts,k∑n

a=1 f ta,k

(3)

wherek∑

a=1

wts,a = 1

which means that the summation of the weights for all kfeatures should be equal to 1.

C. Sig4UDD Game Overview

We design a two-player signaling game that is playedbetween two encountered nodes, Sender and Receiver. Thetype of Sender and Receiver can be either SS or FC thatis private. In particular, we consider a case Sender aimingto forward message m (signal) to Receiver. We assume thatSender selects m from its message list Ms based on theMessage Priority module. Receiver observes m and updates its



belief about the type of Sender based on the properties of m.Then, Receiver takes a feasible action (i.e., accept or drop)regarding m based on its posterior belief. Finally, Sender andReceiver are awarded payoffs based on their type, their action,and the properties of m. The game is played between Senderand Receiver repetitively until the connection is lost or all theirmessages are processed.

D. Game Formulation

We formulate Sig4UDD game by a six-tuplet

G(N, T, A, S, P, U) (4)

which includes the following elements.Players (N): Two encountered nodes are the game players,

which are denoted as Sender and Receiver.Types (T): The set of Sender’s possible type is

Ts = {FC, SS}, where its actual type is denoted as ts .Similarly, the type of Receiver is tr , where its type set isdenoted as Tr = {FC, SS}. We assume that each player onlyknows its own type. We also assume that the type of eachplayer is persistence.

Actions (A): The action profile of Sender is denoted as As ,which is determined based on its type. If ts = FA, thenAs = {Forward}, and if ts = SS, then As = {Forward, Hold}.Similarly, the action profile of Receiver is Ar . If tr = FC, thenAr = {Accept} and if tr = SS, then Ar = {Accept, Drop}.In other words, FC Sender always takes action as = Forward,whereas SS Sender can take either action as = Forward tosend m to Receiver or as = Hold to hold m. In contrast, FCReceiver always takes action ar = Accept to store m, whereasSS Receiver can take either action ar = Accept to store m orar = Drop to reject m.

Strategies (S): This is defined as function ss : Ts → As thatis a mapping from its type into its actions, where ss(ts) ∈ As

is the specific action of the Sender of type ts . However, Sendermay select each pure strategy with a certain probability that iscalled a mixed strategy. A mixed strategy for Sender is iden-tified as ss : Ts × As → [0, 1], such that

∑as∈As

ss(ts |as) = 1for all ts ∈ Ts . In this function, ss(ts |as) is the probabilitythat Sender with type ts takes as ∈ As . In contrast, a purestrategy for Receiver is defined as a function sr : As → Ar ,whereas a mixed strategy sr (as |ar ) for Receiver is definedas sr : As × Ar → [0, 1], where

∑ar ∈Ar

sr (as |ar ) = 1 forall as ∈ As . In this function, sr (as |ar ) is the probability thatReceiver takes action ar following the action as from Sender.

Belief Probabilities (P): is defined as the probabilistic massfunction pr (ts) ∈ [0, 1], which presents the probability thatSender has type ts . Thus, pr (ts = FA) denotes that Sender isan FC node with probability pr , and pr (ts = SS) denotes thatSender is an SS node with probability 1 − pr . In addition,a conditional belief is defined as function pr (ts |as), theprobability that Sender holds type ts if it takes action as .

Payoffs (U): This is defined as the expected payoff of takingan action by a player, given the action and type of anotherplayer. In particular, the expected payoff of Sender relies onher decision that whether she takes action Forward or Holdregarding message m based on her type. Meanwhile, the action

TABLE I

NOTATIONS AND VARIABLES

of Receiver affects Sender’s decision. Thus, the expectedpayoff of Sender can be calculated as follows:

Us(as, ar , ts)

=∑

as∈As

∑ar ∈Ar

ss(ts |as) sr (ar |as) Us(as, ar , ts) (5)

where ss(ts |as) and sr (ar |as) are the probability of choosingmixed strategy ss and sr by Sender and Receiver, respectively.In addition, as and ar are the actions of Sender and Receiver,respectively, and ts is the type of Sender. Note that Senderaims to maximize her expected payoff by selecting her bestresponse that is explained in Section IV-E [see (13)].

On the other side, Receiver makes a decision whether toaccept or reject m, given her type and her belief about thetype of Sender. Therefore, the expected payoff of Receiver is

Ur (as, ar , tr )

=∑ts∈Ts

∑arc∈Ar

pr (ts |as) sr (as |ar ) Ur (as, ar , tr ) (6)

where pr (ts |as) is the posterior belief of Receiver about thetype of Sender, conditional on its action as , and sr (as |ar ) is hermixed strategy. A summary of the game notations is presentedin Table I.

E. One-Stage Equilibrium Analysis

Here, we analyze one-stage equilibrium that implies that theplayers play the game in one round over message m. We firstidentify the utilities and costs of each strategy for the players.Then, we analyze the one-stage game to find the pure andmixed equilibriums.

Fig. 4 shows the extensive form of the game as a tree.First, nature first chooses the type of Sender with probabilityfactor γ . The single strategy available for FC Sender isForward, while it can either take action Forward or Holdif its type is SS. The possible action for SS Receiver canbe either Accept or Drop. The expected payoffs of each purestrategy pairs are shown on the leaves of the tree as (Sender’spayoff and Receiver’s payoff ).



Fig. 4. Extensive form of the game.

1) Expected Payoff in One-Stage Game: We define utility(or gain) G and cost C functions for each pure strategy pairin the one-stage game based on the expected payoff of eachstrategy. The expected payoff of Sender is

Us(ss(ts)) = Gs(ss(ts)) − Cs(ss(ts)) (7)

where Us is equal to the difference between the utility and costfunctions, given the strategy ss chosen by Sender of type ts .Similarly, we define the one-stage expected payoff of Receiver.

Considering that SS nodes aim to maximize their individualand social utilities, we extend (7) as follows:

Gs(ss(ts), m) = αs GSs (ss(ts), m)

+ (1 − αs)GIs (ss(ts), m), 0 ≤ αs ≤ 1 (8)

where GSs and GI

s denote the social and individual utilities ofstrategy ss to Sender of type ts . In addition, αs is a constantfactor that identifies the Sender’s social-awareness degree.In the evaluations, we assigned αs = (1/2), which implies thatSender considers its social utility the same as its individualutility. Similarly, we define the one-stage expected payoffof Receiver. Furthermore, m should satisfy the followingcondition:

maxm∈Ms

(GS

s (ss(ts), m) + GIs (ss(ts), m)

)(9)

subject to

G∗s (ss(ts), m) ≥ ε

where ε is a threshold value that is calculated as

ε =k∑

i=1

Gs(ss(ts), mi )

k(10)

where k is the number of messages in Sender’s buffer.To achieve the maximum utility, the social utility of

forwarding m to Sender is

GSs (ss(ts) = Forward, m)

=⎧⎨⎩

1 − wsdts,src + wsdt

s,des

2, srcm �= Sender

0, otherwise

(11)

TABLE II

UTILITY AND COST PARAMETERS IN ONE-STAGE GAME

where wsdts,src is the WSD between Sender and srcm and

wsdts,des is the WSD between Sender and desm . Furthermore,

the individual utility of m to Sender is

GIs (ss(ts) = Forward, m)

=

⎧⎪⎨⎪⎩

max

(0, 1 − E

[dm

s,r

]

ttlm

), srcm = Sender

0, otherwise

(12)

where dms,r is the average delivery delay of forwarding m from

Sender to Receiver and ttlm is the TTL of m.2) One-Stage Pure Equilibrium Analysis: We use BNE [9]

to analyze the one-stage Sig4UDD game. To this aim, wefirst define the utility and cost parameters of forwardingor receiving m, as shown in Table II. We assume that theutility of forwarding or accepting m is far more than its cost,i.e., Fu � Fc and Au � Ac.

As shown in Fig. 4, the pure strategies of Sender are Ss ={(Forward ∀ Ts), (Forward if ts = FC, Hold if ts = SS)}.Thus, FC Sender can only take action Forward to forward m,while SS Sender can take action Forward or Hold. The strategyset of Receiver is Sr = {Accept, Drop}, which can be chosenbased on its belief. For instance, the expected payoff of actionprofile (as , ar ) = (Forward, Accept) to Sender and Receiveris Fu − Fc and Au − Ac, respectively.

For the given strategy profile Ss and Sr , a BNE is theoptimal strategy profile s∗ = (s∗

s s∗r ), s∗

s ∈ Ss , and s∗r ∈ Sr

that maximizes the expected payoff of Sender and Receiver.Therefore, the best response of Sender should satisfy

s∗s (ts) = max

s∗s ∈Ss

∑ar ∈Ar

ps(s∗

s |ar)Us

(s∗

s (ts), ar , ts)

(13)

where ps(s∗s |ar ) is the belief probability, based on which

Receiver takes action ar ∈ Ar following s∗s . In (13), the

expected payoff is calculated using (5). We define the bestresponse of Receiver using (6) similarly.

We represent the payoff matrices of the one-stage gamein Fig. 5, where Fig. 5(a) and (b), respectively, shows thepayoffs of the players when the type of Sender is FC andSS. We let strategies Ss and Sr are played, and look for acondition under which neither player can maximize its payoffby deviating from s∗. To find BNE, we eliminate some trivialpure strategies and analyze the following cases.

Case 1 [ss = (Forward if ts = SS)]: In this case, we assumethat Sender takes action Forward to send m to Receiver.If Receiver takes action Accept to receive m, its expected



Fig. 5. Payoff matrices of sender and receiver.

payoff is

Ur (Accept) = (1 − pr )(Au − Ac) (14)

where 1 − pr is the belief probability that the type of Senderis SS and Au − Ac is the expected payoff of accepting m.In contrast, if Receiver takes action Drop to reject m, itsexpected payoff is

Ur (Drop) = −Dc(1 − pr ). (15)

If Ur (Accept) ≥ Ur (Drop), the dominant strategy ofReceiver is to take action Accept. Therefore, the pure strategypair (s∗

s s∗r ) = (Forward if ts = SS, Accept) is a BNE when

Au − Ac > −Dc. Considering the assumption Au � Ac, theexpected payoff Au − Ac will be always higher than −Dc.Therefore, the condition Ur (Accept) > Ur (Drop) is satisfied,and therefore, it is a BNE.

If Ur (Drop) > Ur (Accept), the best response of Receiveris to take action Drop given that Au − Ac < −Dc. Therefore,the best response of Sender against action Drop is action Holdwhich does not satisfy assumption Au � Ac, and hence itcannot be a BNE.

Case 2 [ss = (Forward if ts = FC, Hold if ts = SS)]:In this case, we assume that FC Sender plays action Forwardto send m or plays action Hold if its type is SS. Therefore,the expected payoff of strategies Accept if its type is FC orHold if its type is SS to Receiver is

Ur (Accept) = pr (Au − Ac) (16)

where pr is the belief probability with which the type ofSender is FC. Note that action Hold taken by Sender hasno utility for Receiver. In contrast, if Receiver takes Dropto reject m, its expected payoff is

Ur (Drop) = −Dc(1 − pr ). (17)

If Ur (Accept) ≥ Ur (Drop), the dominant strategy ofReceiver is action Accept if Sender forward m. Therefore,(s∗

s s∗r ) = (Forward if ts = FC, Hold if ts = SS, Accept)

is a BNE, given that (pr/1 − pr ) ≥ (−Dc/Au − Ac) and0 ≤ pr < 1. If Ur (Drop) ≥ Ur (Accept), Receiver takesaction Drop to reject m under the condition that (pr/1 − pr ) <(−Dc/Au − Ac). Considering the assumptions Au � Ac and0 ≤ pr ≤ 1, the condition Ur (Drop) ≥ Ur (Accept) is notsatisfied, and hence it cannot be a BNE.

3) One-Stage Mixed Equilibrium Analysis: Despite the factthat the pure strategy BNE exists, the best response of Receiveris to take action Accept. Hence, Receiver will not be ableto deduce the actual type of Sender. This problem is calledPooling Equilibrium [34]. To deal with this problem, we applya mixed-strategy BNE, in which the players choose theirstrategies with a certain probability. We assume that q is theprobability that the SS Sender takes the action Forward andz is the probability that the Receiver takes the action Drop.To find the mixed-strategy BNE, we find q and z in a wayneither Sender nor Receiver can improve their expected payoffby changing their actions. Thus, the expected payoff of playingaction Accept to Receiver is

Ur (Accept) = (1 − z)(1 − pr )(Au − Ac). (18)

If Receiver plays Drop, her expected payoff is

Ur (Drop) = −Dcz(1 − pr ). (19)

To calculate z, we assign Ur (Accept) = Ur (Drop). Thus,we have (z/(1 − z)) = ((1 − pr )(Au − Ac)/−Dc). On theother hand, the expected payoff of SS Sender taking the actionForward is

Us(Forward) = q(1 − pr )(Au − Ac). (20)

If SS Sender takes Hold, her expected utility is

Us(Hold) = −Hc(1 − q). (21)

Therefore, assuming Us(Forward) = Us(Drop), q is calcu-lated as (q/(1 − q)) = (−Hc/(1 − pr )(Au − Ac)).

To sum up the one-stage game analysis, we state thefollowing lemma.

There is a mixed-strategy BNE for Sig4UDD gamewhen (s∗

s , s∗r ) = {(Forward if ts = FC, Hold if ts =

SS with probability z = ((1 − z)(1 − pr )(Au − Ac)/−Dc)),Accept ∀ Tr with probability q = (−Hc(1 − q)/(1 − pr )(Au − Ac))}.

F. Multistage Equilibrium Analysis

1) Belief System: In this section, we introduce Belief Systemto initialize and update the Receiver’s belief about the typeof Sender through their multistage interactions. The BeliefSystem includes two modules: Belief Initialization and BeliefUpdate that are explained as follows.

a) Belief initialization: The belief of Receiver about thetype of Sender is initialized based on their social features whenthey contact each other for the first time. We formalize thebelief initialization of Receiver as follows:

p(t=0)r (ts = SS) = wsdt=0

r,s (22)

where p(t=0)r (ts = SS) is the probability that the type of

Sender is SS and wsdt=0r,s ∈ [0, 1] is the social distance between

Sender and Receiver. In addition, 1 − p(t=0)r (ts = SS) is the

probability that the type of Sender is FC at time stage t = 0.



b) Belief update: Once the belief is initialized, the beliefis updated through a “messagewise” process, which meansthat the properties of m are used by Receiver to update herbelief. Therefore, we calculate the belief of Receiver at timestage t + 1 based on Bayes’ theorem as follows:

p(t+1)r (ts = SS)

= ptr ht

s(as |ts = SS)

ptrht

s(as |ts = SS) + (1 − pt

r

)ht

s(as |ts = FC)(23)

where ptr denotes the posterior belief of Receiver at time t and

hts(as |ts = SS) denotes the probability measure on the history

of SS Sender’s actions at the end of this stage. The termsin (23) are calculated as

hts(as = Forward|ts = SS)

= qp(t)r (ts = SS)

(1 − Min

(wsdt

s,src, wsdts,des

))(24)

and

hts(as = Forward|ts = FC)

= 1 − hts(as = Forward|ts = SS). (25)

2) Perfect Bayesian Equilibrium: PBE is an innovative ideato characterize dependence among the players’ best responsestrategies and their current beliefs. To find PBE in Sig4UDD,we assume an arbitrary stage of the game, say k, where qk isthe probability that SS Sender takes action Forward and zk isthe probability that Receiver takes the action Drop. There-fore, let U (k)

r (Accept) = U (k)r (Drop) and U (k)

r (Forward) =U (k)

r (Drop). Consequently, PBE solutions can be calculatedas follows:

qk = −Hc(1 − qk)

(1−p(k)r (ts = SS))(Au − Ac)

(26)

and

zk = (1 − qk)(1 − pr )(Au − Ac)

−Dc. (27)

As a result, the multistage Sig4UDD game has a PBEwith strategy profile (s∗(k)

s s∗(k)r ) = (qk, zk) that satisfies the

optimality of PBE.

G. Message Handler

The Message Handler includes two modules: the PriorityManager that identifies the forwarding priority of messagesand the Buffer Manager that manages the nodes’ buffer.We apply a simple queuing policy in the Priority Managermodule for FC nodes, in which both the originally generatedand relaying messages are ordered based on their bufferingtime. In contrast, the priority of messages in SS nodes isidentified based on their expected payoff.

The Buffer Manager module manages the buffer of eachnode when it overflows. This module checks the TTL ofmessages and drops expired messages. We employ differentbuffering mechanisms for FC and SS nodes in this module.When the buffer of an FC node overflows, the new incomingmessage is replaced with a message with the lowest TTL.In contrast, when the buffer of an SS node overflows, the

Algorithm 1 SS Sender1: Sender (S) aims to forward its messages to Receiver (R)2: Let Ms denote the list of messages in S3: initialization4: Forward Ft

s to R5: Fetch the feature space of R and set Ft

r6: Compute wsdt

s,r using Fts and Ft

r Equ. 17: end initialization8: loop9: for each m in Ms and m � ∃Mr

10: if srcm= S then11: Forward m to R12: Continue13: end if14: if ts is FC then15: Forward m to R16: else ts is SS17: if Gs(ss(ts))> ε then Equ. 818: Forward m to R19: else20: Hold m21: end if22: end if23: end loop

incoming message is replaced with a message with the lowestexpected payoff. We also design a garbage collection mecha-nism to discard the copies of delivered messages.

H. Uncertain Data Delivery

The routing process between Sender and Receiver is per-formed using the Uncertain Data Delivery component. If thetype of Sender and Receiver is FC, they follow the AltruisticSender/Receiver module to transfer messages from Sender toReceiver. In particular, we employ the Epidemic routing inthis module to forward messages. In contrast, Sender andReceiver with type SS follow the SS Sender/Receiver moduleto, respectively, forward and receive based on Algorithms 1and 2.

Algorithm 1 illustrates the pseudocode of the SS Sendermodule. According to this algorithm, when Sender andReceiver contact each other, Sender and Receiver exchangetheir social features Ft

s and Ftr . Then, Sender calculates

its social distance with Receiver wsdts,r using (1). In this

step, Sender forward m to Receiver if one of the followingconditions is satisfied: 1) if Sender is the source of m or thetype of Sender is FC and 2) if the type of Sender is SS andthe expected payoff Gs(ss(ts)) of m is higher than threshold ε.

Algorithm 2 illustrates the pseudocode of the SS Receivermodule. In this algorithm, Receiver makes a decision based onits type in order to either accept m or drop it. As mentionedin Algorithm 1, when Sender and Receiver contact each other,they exchange their social features Ft

r and Fts . Then, Receiver

calculates its social distance with Sender wsdtr,s to initialize

its belief about the type of Sender (line 6). Then, Receiverapplies the following procedure to process each incoming



Algorithm 2 SS Receiver1: Receiver(R) processes the incoming messages from

Sender(S)2: initialization3: Forward Ft

r to S4: Fetch the feature space of R and set Ft

s5: Compute wsdt

r,s using Ftr and Ft

s Equ. 1

6: Initialize the belief p(t=0)r (ts = SS) Equ. 22

7: end initialization8: loop9: for each incoming message m

10: if desm= R then11: Receive m12: Continue13: end if14: if tr is FC then15: Store m in Mr

16: else tr is SS17: Update p(t+1)

r (ts = SS) Equ. 2318: Calculate the best response s∗

r (tr ) Equ. 619: if The best response of R is Accept then20: Buffer m in Mr

21: else i.e., the best response of R is Drop22: Drop m23: end if24: end if25: end loop

message m and decide whether accept m or drop it. First,Receiver stores m if m is destined to Receiver (line 10). If thetype of Receiver is FC and Receiver is not the destination ofm, it stores m to deliver or forward it to another encounterednode later (line 15). If the type of Receiver is SS, it updatesits belief about the type of Sender based on the properties ofm (line 17). Finally, Receiver makes its best response basedon the mixed BNE to either accept m or drop it.

V. PERFORMANCE EVALUATION

We compare the performance of Sig4UDD against threerouting protocols using the opportunistic network environ-ment (ONE) [35] simulator. The ONE is a trace-driven sim-ulator to evaluate protocols for DTNs. We have two goalsin the experiments. First, we want to evaluate the impact ofthe uncertain cooperation among SS and FC nodes on therouting performance. Second, we compare the performance ofour proposed scheme with some benchmark cooperative andnoncooperative routing protocols.

A. Human Social Data Sets

We use two real-world data sets, MIT Reality Mining [36]and Social Evolution [37], in the experiments. The mainreasons to use these data sets are twofold. First, they containthe real traces of participants for a long period, which areappropriate to evaluate DTN protocols. Second, they includethe Bluetooth and social features of participants that help usto realize the nodes’ contact and social ties. It is, respectively,

TABLE III

PROPERTIES OF THE DATA SETS

verified in [36] and [37] that the contact and social features ofparticipants in these data sets have social behavior embedded.To import these data sets to the ONE, we first process themin MATLAB and then convert them into a format compatiblewith the ONE.

1) Reality Mining: This data set includes the contact andsocial statistics of 106 users, which carry Nokia 6600 smart-phones preinstalled with some pieces of the developed soft-ware. We filter a part of the trace between October 2004and April 2005. In addition, we discard the information ofparticipants with insufficient contact and social features andselect 88 out of 106 participants in the experiments. Sincethe original data set does not provide the subjects’ WLANlocation information, we use 48% of unique cell locationsin [38]. We select four features for the experiments as follows:1) Bluetooth contact frequency; 2) affiliation; 3) visited loca-tions; and 4) call and SMS logs.

2) Social Evolution: This data set includes the contact andsocial information of 80 undergraduate students that carry theirphones for 8 months. We select 74 out of 80 subjects betweenJanuary and June 2009 in the experiments. Furthermore, weextract four features for the experiments as follows: 1) Blue-tooth contact frequency; 2) interests (e.g., music); 3) subjects(living sector); and 4) call and SMS logs. Table III summarizesthe features of the data sets.

B. Simulation Settings and Performance Metrics

In the experiments, we consider a mobile wireless networkwhere the transmission speed of the Bluetooth interface is5 MB/s. We study the impact of changing the messageTTL, buffer capacity, and the ratio of selfish nodes on therouting performance. Messages with a random size from500 kB to 1 MB and a uniform interval of 15∼20 h aregenerated for each node. Furthermore, TTL of messages variesbetween 1 day and 30 days. The buffer of nodes varies between2 and 30 MB. Each simulation is run 10 times with differentrandom seeds to provide results with high confidence.

We evaluate four metrics in our simulations as follows.1) Average Delivery Delay: The average time that it takes

a message to be delivered to its destination.2) Average Delivery Cost: The proportion of the total

number of replicated messages (including control mes-sages, social information, and dropped messages) to thenumber of delivered messages.

3) Average Delivery Ratio: The proportion of the numberof delivered messages to the total number of generatedmessages.



Fig. 6. Performance comparisons of the algorithms with changing the TTL of messages (d = day and w = week). (a) Delivery delay, Reality Mining.(b) Delivery cost, Reality Mining. (c) Delivery ratio, Reality Mining. (d) Delivery delay, Social Evolution. (e) Delivery cost, Social Evolution.(f) Delivery ratio, Social Evolution.

C. Algorithms in Comparison

We benchmark Sig4UDD against two cooperative and twononcooperative routing protocols as follows.

1) Epidemic [10]: A flooding-based cooperative protocolin which two encountered nodes replicate the copy oftheir messages to each other those they have not receivedbefore.

2) dLife [15]: A social-based cooperative protocol in whichthe strength of social ties among nodes are exploited toselect the intermediate nodes.

3) SSAR [7]: A SS-aware routing in which selfish nodesforward messages to the nodes with strong social ties.

4) Ind-Self [17]: A noncooperative protocol in which nodesonly forward their own messages.

D. Evaluations

1) Impact of Varying the Message TTL: As shown in Fig. 6,we compare the algorithms when the TTL of messages variesbetween 1 and 2 days and 1, 2, 3, and 4 weeks. The bufferof each node is 15 MB. In Epidemic and dLife, 100% ofnodes are FC. Based on the results in [17], we assume that70% of nodes are selfish in SSAR and Sig4UDD and the restof the nodes are FC. The reason is that DTNs well toleratequite a large number of selfish nodes (20%–40% or even 60%)without too much harm. We also assume that 70% of the nodesin Ind-Self are IS and 30% of the remaining nodes are FC.

Fig. 6(a) compares the algorithms in the message deliverydelay on the Reality Mining data set. As the TTL of themessages increases, the delivery delay of the algorithms shows

a continuous upward trend, because messages stay longer inthe network. Among the algorithms, Ind-Self has the longestdelivery delay, whereas Epidemic has the shortest delay.Comparatively, Sig4UDD has a shorter delivery delay thanthe noncooperative protocols (i.e., Ind-Self and SSAR), whileits delivery delay is longer than the cooperative protocols. Forexample, when the TTL of messages is 3 weeks, Sig4UDDoutperforms Ind-Self and SSAR by 60% and 18%, respec-tively. This is because Sig4UDD identifies the best responsesof SS intermediate nodes based on their expected payoffs andthe beliefs. Thus, the SS sender nodes in sig4UDD forwardmessages that will be accepted by the SS receivers with ahigh probability. Consequently, the messages in Sig4UDD aredelivered to the destinations with a short delay in comparisonwith the other noncooperative protocols. However, the defi-ciency of Sig4UDD against Epidemic and dLife is because allthe nodes in Epidemic and dLife are FC and participate inmessage delivery.

Fig. 6(b) compares the message delivery cost of the algo-rithms on the Reality Mining data set. As the TTL of themessages increases, the delivery cost in all the algorithmsrises gradually. Among the algorithms, Sig4UDD has thelowest message delivery cost, whereas Ind-Self has the highestdelivery cost. For example, when the TTL of messages is3 weeks, Sig4UDD outperforms Ind-Self, Epidemic, dLife,and SSAR by 300%, 230%, 35%, and 20%, respectively.The main reason is that SS nodes in Sig4UDD take thewillingness of relaying nodes about carrying each message intoaccount and forward those messages that more likely wouldbe accepted by them.



Fig. 7. Performance comparisons of the algorithms with changing the buffer size. (a) Delivery delay, Reality Mining. (b) Delivery cost, Reality Mining.(c) Delivery ratio, Reality Mining. (d) Delivery delay, Social Evolution. (e) Delivery cost, Social Evolution. (f) Delivery ratio, Social Evolution.

In comparison with the other protocols, the performance ofSig4UDD in terms of the message delivery delay and costis not achieved complimentary. As shown in Fig. 6(c), theaverage delivery ratio of Sig4UDD is less than Epidemic,dLife, and SSAR, although Sig4UDD has still better deliveryratio than Ind-Self. The main reason for the deficiency ofSig4UDD in this metric is that SS nodes sometimes decideto hold messages rather than forwarding them to the nextintermediate nodes that may have better opportunities tocontact the destinations. This is because the beliefs of nodesmay not be accurate about the type of other nodes. Fig. 6(d)–(f)shows the evaluations of the algorithms conducted on theSocial Evolution data set that follows the similar trend withthe results taken from the Reality Mining data set.

2) Impact of Varying the Buffer Capacity: Fig. 7 shows theperformance of the algorithms when the nodes’ buffer sizeis 2, 5, 10, 15, 20, and 25 MB and the TTL of messagesis 15 days.

Fig. 7(a) compares the algorithms in term of the messagedelivery delay on the Reality Mining data set. When thebuffer of nodes increases from 2 to 15 MB, an upwardtendency can be seen in the delivery delay of the algorithms.Comparatively, Sig4UDD has a lower delivery delay thanInd-Self and SSAR. For example, when the buffer is 20 MB,Sig4UDD outperforms Ind-Self and SSAR by 72% and 11%,respectively. The reason is that the beliefs of receiver nodesin Sig4UDD are evolved in a way that they display selfishbehavior toward nodes with dissimilar social features. How-ever, the average delivery delay of Sig4UDD is still longerthan Epidemic and dLife.

Fig. 7(b) shows the average delivery cost on the Real-ity Mining data set. As the buffer of nodes increases,

Sig4UDD outperforms the other protocols with the lowestdelivery cost. For example, when the buffer size of nodesis 15 MB, Sig4UDD outperforms Ind-Self, Epidemic, dLife,and SSAR by 290%, 220%, 30%, and 18%, respectively.This is because SS nodes in Sig4UDD hold some messages,rather than replicating them to some socially dissimilar nodesthat do not have a better opportunity to meet destinationnodes.

Fig. 7(c) shows the average delivery ratio on Reality Mining.Through the whole trend, Epidemic has the highest deliveryratio, whereas Ind-Self has the lowest delivery ratio. However,the performance of Sig4UDD regarding the delivery delay andcost does not come for free, because the delivery ratio inSig4UDD is worse than Epidemic, dLife, and SSAR. The mainreason is that the source and destination of some messages mayhave dissimilar social features. Thus, those messages might bedropped by SS intermediate nodes. Similar performance resultsare found for the algorithms using Social Evolution data set,as shown in Fig. 7(d)–(f).

3) Impact of Varying the Number of Selfish Nodes: In Fig. 8,we compare Sig4UDD with Ind-Self and SSAR when thepercentage of selfish nodes varies between 25% and 100%.In these experiments, the TTL of messages is 15 days and thebuffer size is 15 MB.

Fig. 8(a) compares the algorithms in the average deliverydelay. It can be observed that Sig4UDD has the shortest deliv-ery delay, while Ind-Self has the longest delay. For instance,when 100% of nodes are selfish, Sig4UDD outperforms Ind-Self and SSAR by 53% and 11% using Reality Mining andby 55% and 10% using Social Evolution. As the number ofselfish nodes increases, the delivery delay of Ind-Self risessharply, while the delivery delay of Sig4UDD and SSAR



Fig. 8. Performance comparisons of the noncooperative algorithms with different percent of selfish nodes. (a) Delivery delay. (b) Delivery cost. (c) Deliveryratio.

increases gradually. The reason is that IS nodes in Ind-Selfonly deliver their messages to the destination nodes while SSnodes in Sig4UDD carry the messages received from theirsocially connected nodes.

Fig. 8(b) shows the results in the average delivery cost.Throughout the trend, Sig4UDD has the lowest delivery cost,while Ind-Self has the highest cost. As the number of selfishnodes increases, the delivery cost of Ind-Self goes up swiftly,while a gradual upward trend can be seen in the delivery costof Sig4UDD and SSAR algorithms. Using Reality Miningand Social Evolution and when 100% of nodes are selfish,Sig4UDD outperforms Ind-Self by 230% and 13% and SSARby 220% and 11%, respectively.

Fig. 8(c) compares the algorithms in terms of the averagedelivery ratio. For different percentages of selfish nodes, thedelivery ratio of Sig4UDD is slightly lower than SSAR, whileit is still considerably higher than Ind-Self. As the number ofselfish nodes increases, a constant reduction can be seen inthe delivery ratio of Sig4UDD and SSAR, while the deliveryratio of Ind-Self declines dramatically. For example, when thepercentage of selfish nodes increases from 50% to 100%, theaverage delivery ratio decreases from 0.66 to 0.46 in Sig4UDDand from 0.68 to 0.52 in SSAR. In contrast, the delivery ratioof Ind-Self drops from 0.51 to 0.11 when the percentage ofselfish nodes increases from 50% to 100%. The main reasonis that as the number of SS nodes increases, some messagesmay go through several Sig4UDD game until they are finallydelivered to the destination. Under these circumstances, someSS intermediate nodes may decide to hold the messages ratherthat forwarding them that decreases the delivery ratio ofSig4UDD.

VI. CONCLUSION

In this paper, we proposed Sig4UDD, a belief-based sig-naling game to realize uncertain data delivery among well-behaved and SS nodes in mobile social networks (MSNs).Using real-world data sets, the performance of Sig4UDD wascompared with some benchmark protocols. Our experimentsdemonstrated that Sig4UDD outperforms the other protocolsregarding message delivery cost while the message deliverydelay in Sig4UDD is only shorter than the noncooperativeprotocols. However, the performance of Sig4UDD in terms

of message delivery delay and communication cost does notcome for free, because the message delivery ratio in Sig4UDDis worse than the other algorithms. As an extension, weplan to design a game-theoretic incentive scheme to stimulateSS nodes to cooperate in message delivery with sociallydissimilar nodes.

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Feng Xia (M’07–SM’12) received the B.Sc. andPh.D. degrees from Zhejiang University, Hangzhou,China.

He is currently a Full Professor with the Schoolof Software, Dalian University of Technology,Dalian, China. He has published two books andover 200 scientific papers in international journalsand conferences. His current research interestsinclude computational social science, big data, andmobile social networks.

Dr. Xia is a Senior Member of the Association forComputing Machinery.

Behrouz Jedari received the B.Sc. andM.Sc. degrees from Islamic Azad University,Qazvin, Iran, in 2006 and 2009, respectively. He iscurrently pursuing the Ph.D. degree with the Schoolof Software, Dalian University of Technology,Dalian, China.

His current research interests include delay-tolerant networks, social network analysis, andmobile social networks.

Laurence Tianruo Yang received the B.E. degreein computer science and technology from TsinghuaUniversity, Beijing, China, and the Ph.D. degree incomputer science from the University of Victoria,Victoria, BC, Canada.

He is currently a Professor with the Departmentof Computer Science, St. Francis Xavier University,Antigonish, NS, Canada. His current research inter-ests include parallel and distributed computing andembedded and ubiquitous/pervasive computing.

Jianhua Ma received the M.S. degree from theNational University of Defense Technology, Chang-sha, China, in 1985, and the Ph.D. degree fromXidian University, Xi’an, China, in 1990.

He is currently a Professor with the Faculty ofComputer and Information Sciences, Hosei Univer-sity, Tokyo, Japan. He has published over 200 papersand edited over 20 books/proceedings and over20 journal special issues. His current research inter-ests include multimedia, networks, ubiquitous com-puting, social computing, and cyber intelligence.

Runhe Huang received the Ph.D. degree in com-puter science and mathematics from the Universityof the West of England, Bristol, U.K., in 1993.

She is currently a Full Professor with the Facultyof Computer and Information Sciences, Hosei Uni-versity, Tokyo, Japan. Her current research interestsinclude multiagent systems, computational intelli-gence computing, ubiquitous intelligence computing,and big data.

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