IEEE TRANSACTIONS ON MOBILE COMPUTING, …people.cs.vt.edu/~irchen/6204/pdf/Saad-TMC11.pdf · Index Terms—Multiagent wireless networks, game theory, hedonic coalitions, task allocation,

Hedonic Coalition Formation for DistributedTask Allocation among Wireless Agents

Walid Saad, Zhu Han, Senior Member, IEEE, Tamer Basar, Fellow, IEEE,

Merouane Debbah, and Are Hjørungnes, Senior Member, IEEE

Abstract—Autonomous wireless agents such as unmanned aerial vehicles, mobile base stations, cognitive devices, or self-operating

wireless nodes present a great potential for deployment in next-generation wireless networks. While current literature has been mainly

focused on the use of agents within robotics or software engineering applications, this paper proposes a novel usage model for self-

organizing agents suitable for wireless communication networks. In the proposed model, a number of agents are required to collect

data from several arbitrarily located tasks. Each task represents a queue of packets that require collection and subsequent wireless

transmission by the agents to a central receiver. The problem is modeled as a hedonic coalition formation game between the agents

and the tasks that interact in order to form disjoint coalitions. Each formed coalition is modeled as a polling system consisting of a

number of agents, designated as collectors, which move between the different tasks present in the coalition, collect and transmit the

packets. Within each coalition, some agents might also take the role of a relay for improving the packet success rate of the

transmission. The proposed hedonic coalition formation algorithm allows the tasks and the agents to take distributed decisions to join

or leave a coalition, based on the achieved benefit in terms of effective throughput, and the cost in terms of polling system delay. As a

result of these decisions, the agents and tasks structure themselves into independent disjoint coalitions which constitute a Nash-stable

network partition. Moreover, the proposed coalition formation algorithm allows the agents and tasks to adapt the topology to

environmental changes, such as the arrival of new tasks, the removal of existing tasks, or the mobility of the tasks. Simulation results

show how the proposed algorithm allows the agents and tasks to self-organize into independent coalitions, while improving the

performance, in terms of average player (agent or task) payoff, of at least 30.26 percent (for a network of five agents with up to

25 tasks) relatively to a scheme that allocates nearby tasks equally among agents.

Index Terms—Multiagent wireless networks, game theory, hedonic coalitions, task allocation, ad hoc networks.

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1 INTRODUCTION

NEXT-GENERATION wireless networks will present a highlycomplex and dynamic environment characterized by a

large number of heterogeneous information sources, and avariety of distributed network nodes. This is mainly due tothe recent emergence of large-scale, distributed, andheterogeneous communication systems which are continu-ously increasing in size, traffic, applications, services, etc.For maintaining a satisfactory operation of such networks,there is a constant need for dynamically optimizing theirperformance, monitoring their operation, and reconfiguringtheir topology. Due to the ubiquitous nature of such

wireless networks, it is inherent to have self-organizingautonomous nodes (agents) that can service these networksat different levels, such as data collection, monitoring,optimization, management, maintenance, among others [1],[2], [3], [4], [5], [6], [7], [8]. These nodes belong to theauthority maintaining the network, and must be able tosurvey large-scale networks, and perform very specifictasks at different points in time, in a distributed andautonomous manner, with very little reliance on anycentralized authority [1], [2], [3], [6], [7], [8].

While the use of such autonomous agents has beenthoroughly investigated in robotics, computer systems orsoftware engineering, research models that tackle the use ofsuch agents in wireless communication networks are few.However, recently, the need for such agents in wirelessnetworks has become of noticeable importance as manynext-generation networks encompass several wireless nodetypes, such as cognitive devices or unmanned aerialvehicles, that are autonomous and self-adapting [1], [2],[3], [4], [5], [6], [7], [8]. A key problem in this context is theproblem of task allocation among a group of agents thatneed to execute a number of tasks. This problem has beenalready tackled in areas, such as robotics control [9], [10],[11] or software systems [12], [13]. However, most of theseexisting models are unsuitable for task allocation problemsin the context of wireless networks due to various reasons:1) The task allocation problems studied in the existingpapers are mainly tailored for military operations, compu-ter systems, or software engineering and, thus, cannot bereadily applied in models pertaining to wireless networks,

IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 10, NO. 9, SEPTEMBER 2011 1327

. W. Saad is with the Electrical and Computer Engineering Department,University of Miami, Coral Gables, FL. E-mail: [email protected].

. Z. Han is with the Electrical and Computer Engineering Department,University of Houston, N324, Engineering Building 1, Houston, TX77004, and is also with the Department of Electronics and RadioEngineering, Kyung Hee University, South Korea.E-mail: [email protected].

. T. Basar is with the Coordinated Science Laboratory, University of Illinoisat Urbana-Champaign, 1308 West Main, Urbana, IL 61801.E-mail: [email protected].

. M. Debbah is with SUP �ELEC, 3 rue Joliot-Curie, Gif-sur-Yvette, France.E-mail: [email protected].

. A. Hjørungnes was with the UNIK University Graduate Center,University of Oslo, Gunnar randers vei 19, Kjeller 2027, Norway. Hepassed away in May 2011.

Manuscript received 8 June 2009; revised 7 Oct. 2010; accepted 19 Oct. 2010;published online 17 Dec. 2010.For information on obtaining reprints of this article, please send e-mail to:[email protected], and reference IEEECS Log Number TMC-2009-06-0215.Digital Object Identifier no. 10.1109/TMC.2010.242.

1536-1233/11/$26.00 � 2011 IEEE Published by the IEEE CS, CASS, ComSoc, IES, & SPS

2) the tasks are generally considered as static abstractentities with very simple characteristics and no intelligence(e.g., the tasks are just points in a plane) which is a majorlimitation, and 3) the existing models do not consider anyaspects of wireless communication networks, such as thecharacteristics of the wireless channel, the presence of datatraffic, the need for wireless data transmission, or otherwireless-specific specifications. In this context, numerousapplications in next-generation wireless networks require anumber of agent-nodes to perform specific wireless-relatedtasks that emerge over time and are not preassigned. Oneexample of these applications is the case where a number ofwireless nodes are required to monitor the operation of thenetwork or perform relaying at different times and locations[1], [2], [4], [5], [6], [7], [8]. In such applications, the objectiveis to provide algorithms that allow the agents to autono-mously share the tasks among each other. The main existingcontributions within wireless networking in this area [14],[15], [16], [17], [18], are focused on deploying unmannedaerial vehicles (UAVs) which can act as self-deployingautonomous agents that can efficiently perform preassignedtasks in numerous applications, such as connectivityimprovement in ad hoc network [15], routing [16], [17],and medium access control [18]. However, these contribu-tions focus on centralized solutions for specific problemssuch as finding the optimal locations for the deployment ofUAVs or devising efficient routing algorithms in ad hocnetworks in the presence of UAVs (one or more). Moreover,in these papers, the tasks that the agents must accomplishare preassigned and predetermined. In contrast, as previouslymentioned, many applications in wireless networks requirethe agents to autonomously assign the tasks amongthemselves. Hence, it is inherent to devise algorithms, inthe context of wireless networks, that allow an autonomousand distributed task allocation process among a number ofwireless agents1 with little reliance on centralized entities.

The main contribution of this paper is to propose a novelwireless communication-oriented model for the problem oftask allocation among a number of autonomous agents. Theproposed model considers a number of wireless agents thatare required to collect data from arbitrarily located tasks.Each task represents a source of data, i.e., a queue with aPoisson arrival of packets, that the agents must collect andtransmit via a wireless link to a central receiver. Thisformulation is deemed suitable to model several problemsin next-generation networks such as video surveillance inwireless networks, self-deployment of mobile relays in IEEE802.16j networks [2], data collection in ad hoc and sensornetworks [8], operation of mobile base stations in vehicularad hoc networks [6] and mobile ad hoc networks [7] (the so-called message ferry operation), wireless monitoring ofrandomly located sites, autonomous deployment of un-manned air vehicles in military ad hoc networks, and manyother applications. For allocating the tasks, we introduce anovel framework from coalitional game theory, known ashedonic coalition formation. Albeit hedonic games have beenwidely used in game theory, to the best of our knowledge,no existing work utilized this framework in a communica-tion or wireless environment. Thus, we model the task

allocation problem as a hedonic coalition formation gamebetween the agents and the tasks, and we introduce analgorithm for forming coalitions. Each formed coalition ismodeled as a polling system consisting of a number ofagents, designated as collectors, which act as a single serverthat moves continuously between the different tasks(queues) present in the coalition, gathering and transmittingthe collected packets to a common receiver. Further, withineach coalition, some agents can act as relays for improvingthe packet success rate during the wireless transmission.For forming coalitions, the agents and tasks can autono-mously make a decision to join or leave a coalition based onwell-defined individual preference relations. These prefer-ences are based on a coalitional value function that takesinto account the benefits received from servicing a task, interms of effective throughput (data collected), as well as thecost in terms of the polling system delay incurred from thetime needed for servicing all the tasks in a coalition. Westudy the properties of the proposed algorithm, and showthat it always converges to a Nash-stable network partition.Further, we investigate how the network topology can self-adapt to environmental changes, such as the deployment ofnew tasks, the removal of existing tasks, and low mobilityof the tasks. Simulation results show how the proposedalgorithm allows the network to self-organize, whileensuring a significant performance improvement, in termsof average player (task or agent) payoff, compared to ascheme that assigns nearby tasks equally among the agents.

The remainder of this paper is organized as follows:Section 2 presents and motivates the proposed systemmodel. In Section 3, we model the task allocation problemas a transferable utility coalitional game and propose asuited utility function. In Section 4, we classify the taskallocation coalitional game as a hedonic coalition formationgame, discuss its key properties, and introduce thealgorithm for coalition formation. Simulation results arepresented, discussed, and analyzed in Section 5. Finally,conclusions are drawn in Section 6.

2 SYSTEM MODEL

Consider a network consisting of M wireless agents thatbelong to a single network operator and that are controlledby a central command center (e.g., a central controller nodeor a satellite system). These agents are required to service Ttasks that are arbitrarily located in a geographic area havingan associated central wireless receiver connected to thecommand center. The tasks are entities that, in general,belong to one or more independent owners.2 These tasks’owners can be, for example, service providers or third-partyoperators. We denote the set of agents and tasks by M¼f1; . . . ;Mg and T ¼ f1; . . . ; Tg, respectively. In this paper,we consider only the case where the number of tasks islarger than the number of agents, hence T > M. The mainmotivation behind this consideration is that, for mostnetworks, the number of agents assigned to a specific areais generally small due to cost factors for example. Each taski 2 T represents an M/D/1 queuing system,3 wherebypackets of constant size B are generated using a Poisson

1328 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 10, NO. 9, SEPTEMBER 2011

1. The term wireless agent refers to any node that can act autonomouslyand can perform wireless transmission. Examples of wireless agents areunmanned aerial vehicles [15], mobile base stations [6], [7], [8], cognitivewireless devices [3], or self-deploying mobile relay stations [2].

2. The scenario where all tasks and agents are owned by the same entityis a particular case of this generic model.

3. Other types of queues, e.g., M/M/1, can also be considered withoutloss of generality in the coalition formation process proposed in this paper.

arrival with an average arrival rate of �i. Hence, in theproposed model, we consider different classes of tasks eachhaving its corresponding �i. The tasks we consider aresources of data that cannot send their information to thecentral receiver (and, subsequently, to the command center)without the help of an agent. These tasks can represent agroup of mobile devices, such as sensors, video surveillancedevices, or any other static or dynamic wireless nodes thathave limited power and are unable to provide long-distancetransmission. Hence, these devices (tasks) need to buffertheir data locally and await to be serviced by an agent thatcan collect the data. For example, an agent such as a mobilebase station, a mobile relay, or a UAV can provide a line ofsight link that can facilitate the transmission from the tasksto the central receiver. The tasks can also be mapped to anyother source of packet data that require collection by anagent for transmission.4 For servicing a task, each agent isrequired to move to the task location, collect the data, andtransmit it using a wireless link to the central receiver. Thecommand center periodically downloads these data fromthe receiver, e.g., through a backbone network. Each agenti 2 M offers a link transmission capacity of �i, in packets/second, with which the agent can service the data fromany task. Hence, the quantity 1

�iwould represent the well-

known service time for a single packet that is being servicedby agent i. The agent which is collecting the data from atask is referred to as collector. In addition, each agent i 2 Mcan transmit the data to the receiver with a maximumtransmit power of Pi ¼ ~P , assumed the same for all agents.5

The proposed model allows each task to be serviced bymultiple agents, and also, each agent (or group of agents) toservice multiple tasks. Whenever a task is serviced bymultiple agents, each agent can act as either a collector or arelay. Any group of agents that act together for datacollection from the same task can be seen as a singlecollector with improved link transmission capacity. In thispaper, we consider that the link transmission capacitydepends solely on the capabilities of the agents and not onthe nature of the tasks. In this context, given a group ofagents G �M that are acting as collectors for any task, thetotal link transmission capacity with which tasks can beserviced with by G can be given by

�G ¼Xj2G

�j: ð1Þ

For forming a single collector, multiple agents can easilycoordinate the data extraction, and then transmission fromevery task, so as to allow a larger link transmission capacityfor the serviced task as per (1). Moreover, the transmissionof the packets by the agents from a task i 2 T to the centralreceiver is subject to packet loss due to the fading on thewireless channel. In this regard, in addition to acting ascollectors, some agents may act as relays for a task. Theserelay-agents would locate themselves at equal distancesfrom the task (given that the task is already being served byat least one collector), and hence, the collectors transmit thedata to the receiver through multihop agents, improving theprobability of successful transmission. In this context, in

Rayleigh fading, the probability of successful transmissionof a packet of size B bits from the collectors present at a taski 2 T through a path of m agents, Qi ¼ fi1; . . . ; img, wherei1 ¼ i is the task being serviced, im is the central receiver(CR), and any other ih 2 Qi is a relay-agent, can be given by

Pri;CR ¼Ym�1

h¼1

PrBih;ihþ1; ð2Þ

where Prih;ihþ1is the probability of successful transmission

of a single bit from agent ih to agent (or the central receiver)ihþ1. This probability can be given by the probability ofmaintaining the SNR at the receiver above a target level �0

as follows [19]:

Pri;ihþ1¼ exp ��

2�0ðDih;ihþ1Þ�

� ~P

� �; ð3Þ

where �2 is the variance of the Gaussian noise, � is a pathloss constant, � is the path loss exponent, Dih;ihþ1

is thedistance between nodes ih and ihþ1, and ~P is the maximumtransmit power of agent ih.

For servicing a number of tasks C � T , a group of agentsG �M (collectors and relays) can sequentially move fromone task to the other in C with a constant velocity �. Thegroup G of agents, servicing the tasks in C, stop at each task,with the collectors collecting and transmitting the packetsusing the relays (if any). The collectors would move fromone task to the other, only if all the packets in the queue atthe current task have been transmitted to the receiver (theprocess through which the agents move from one task tothe other for data collection is cyclic). Simultaneously withthe collectors, the relays also move, positioning themselvesat equal distances on the line connecting the task beingcurrently served by the collectors, and the central receiver.With this proposed model, the final network will consist ofgroups of tasks serviced by groups of agents, continuously.An illustration of this model is shown in Fig. 1.

Consequently, given this proposed model, the mainobjective is to provide an algorithm for distributing thetasks between the agents, given the operation of the agentspreviously described and shown in Fig. 1. In other words,the main goal is to allow the agents and task to autono-mously form the coalitional structure in Fig. 1 and adapt itto environmental changes. For this purpose, the followingsections formulate a game-theoretic approach for achievingthis objective.

3 COALITIONAL GAME FORMULATION

In this section, we model the proposed problem as acoalitional game with transferable utility, and propose asuitable utility function.

3.1 Game Formulation

By inspecting Fig. 1, one can clearly see that the taskallocation problem among the agents can be mapped intothe problem of the formation of coalitions. In this regard,coalitional game theory [20, Ch. 9] provides a suitableanalytical tool for studying the formation of cooperativegroups, i.e., coalitions, among a number of players. Forthe proposed model, the coalitional game is played betweenthe agents and the tasks. Hence, the players set for theproposed task allocation coalitional game is denoted by N ,

SAAD ET AL.: HEDONIC COALITION FORMATION FOR DISTRIBUTED TASK ALLOCATION AMONG WIRELESS AGENTS 1329

4. The tasks can be moving with a periodic low mobility, as will be seenin later sections.

5. Note that different maximum transmit power values can be easilyaccommodated in the coalition formation algorithm proposed in the nextsections.

and contains both agents and tasks, i.e., N ¼M[ T . In theremainder of this paper, we use the term player to indicateeither a task or an agent.

For any coalition S � N containing a number of agentsand tasks, the agents belonging to this coalition canstructure themselves into collectors and relays. Subse-quently, as explained in the previous section, within eachcoalition, the collector-agents will continuously move fromone task to the other, stopping at each task, and transmit-ting all the packets available in the queue to the centralreceiver, through the relay-agents (if any). This proposedtask servicing scheme can be mapped to a well-knownconcept that is ubiquitous in computer systems, which isthe concept of a polling system [21]. In a polling system, asingle server moves between multiple queues in order toextract the packets from each queue, in a sequential andcyclic manner. Models pertaining to polling systems havebeen widely developed in various disciplines ranging fromcomputer systems to communication networks, and differ-ent strategies for servicing the queues exist [21], [22], [23],[24]. In the proposed task allocation model, the collectors ofevery coalition in our model are considered as a singleserver that is servicing the tasks (queues) sequentially, in acyclic manner, i.e., after servicing the last task in a coalitionS � N , the collectors of S return to the first task in S thatthey previously visited hence repeating their route con-tinuously. Further, whenever the collectors stop at any taski 2 S, they collect and transmit the data present at this taskuntil the queue is empty. This method of allowing theserver to service a queue until emptying the queue isknown as the exhaustive strategy for a polling system, whichis applied at the level of every coalition S � N in ourmodel. Moreover, the time for the server to move from onequeue to the other is known as the switchover time.Consequently, we highlight the following property:

Property 1. In the proposed task allocation model, every coalitionS � N is a polling system with an exhaustive polling

strategy and deterministic nonzero switchover times. In eachsuch polling system S, the collector-agents are seen as thepolling system server, and the tasks are the queues that thecollector-agents must service.

Furthermore, for any coalition S, once the queue at a taski 2 S is emptied, the collectors and relays in a coalitionmove from task i to the next task j 2 S with a constantvelocity �, hence, incurring a switchover time i;j. Theswitchover time in our model corresponds to the time ittakes for all the agents (collectors and relays) to move fromone task to the next, which, assuming all agents start theirmobility at the same time, maps to the time needed for thefarthest agent to move from one task to the next. Since weconsider only straight line trajectories for collectors andrelays, and due to the fact that the relays always positionthemselves at equal distances on the line connecting thetasks in a coalition to the receiver, we have the followingproperty (clearly seen through the geometry of Fig. 1):

Property 2. Within any given coalition S, the switchover timebetween two tasks corresponds to the constant time it takes forone of the collectors to move from one of the tasks to the next.

Having modeled every coalition S � N as a pollingsystem, we investigate the average delay incurred percoalition. In fact, for polling systems, finding exact expres-sions for the delay at every queue is a highly complicatedtask, and hence, no general closed-form expressions for thedelay at every queue in a polling system can be found[21], [22].6 In this regard, a key criterion used for the analysisof the delay incurred by a polling system is the pseudocon-servation law which provides closed-form expressions forweighted sum of the means of the waiting times at the queues


Fig. 1. An illustrative example of the proposed model for task allocation in wireless networks (the agents are dynamic, i.e., they move from one taskto the other continuously).

6. Note that some approximations [22] exist for polling systems underheavy traffic or large switchover times, but in our problem, they are notsuitable as we require a more general delay expression.

[21], [22]. For providing the pseudoconservation law for acoalition S � N composed of a number of agents and anumber of tasks, we make the following definitions. First,within coalition S, a group of agents GS � S \M aredesignated as collectors. Second, for each task i 2 S \ Twith an average arrival rate of �i, and served by a number ofcollectors jGS j with a link transmission capacity of �GS (asgiven by (1)), we define the utilization factor of task ii ¼ �i

�GS.

Further, we define S ¼4P

i2S\T i. Given these definitions,for a coalition S, the weighted sum of the means of thewaiting times by the agents at all the tasks in the coalition aregiven by the pseudoconservation law, [22, Section. 6.2](taking into account that our switchover and service timesare deterministic), as follows:

Xi2S\T

i �Wi ¼ S

Pi2S\T

i�GS

2ð1� SÞþ S

2S

2

þ S2ð1� SÞ

2S �

Xi2S\T

2i

" #;

ð4Þ

where �Wi is the mean waiting time at task i and S ¼PjS\T jh¼1 ih;ihþ1

is the sum of the switchover times given a pathof tasks fi1; . . . ; ijS\T jg followed by the agents, with ih 2S \ T ; 8 h 2 f1; . . . ; jS \ T jg and ijS\T jþ1 ¼ i1. The first termin the right-hand side of (4) is the well-known expressionfor the average queuing delay for M/D/1 queues, weighedby S . The second and third terms in the right-hand side of(4) represent the average delay increase incurred by thetravel time required for the collectors to move from one taskto the other, i.e., the delay resulting from the switchoverperiod. Further, for any coalition S that must form in thesystem, the following condition must hold:

S < 1: ð5Þ

This condition is a requirement for the stability of anypolling system [21], [22], [23], [24] and, thus, must be satisfiedfor any coalition that will form in the proposed model. Inthe event where this condition is violated, the system isconsidered unstable and the delay is considered as infinite.In this regard, the analysis presented in the remainder ofthis paper will take into account this condition and itsimpact on the coalition formation process (as demonstratedin the next sections, a coalition where S � 1 will never form).

3.2 Utility Function

In the proposed game, for every coalition S � N , the agentsmust determine the order in which the tasks in S are visited,i.e., the path fi1; . . . ; ijS\T jgwhich is an ordering over the setof tasks in S given by S \ T . Naturally, the agents mustselect the path that minimizes the total switchover time forone round of data collection. This can be mapped to thefollowing well-known problem:

Property 3. The problem of finding the path that minimizes thetotal switchover time for one round of data collection within acoalition S � N is mapped into the traveling salesmanproblem [25], where a salesman, i.e., the agents S \M, isrequired to minimize the time of visiting a series of cities, i.e.,the tasks S \ T .

It is widely known that the solution for the travelingsalesman problem is NP-complete [25], and hence there has

been numerous heuristic algorithms for finding an accep-table near-optimal solution. One of the simplest of suchalgorithms is the nearest neighbor algorithm (also known asthe greedy algorithm) [25]. In this algorithm, starting from agiven city the salesman chooses the closet city as his nextvisit. Using the nearest neighbor algorithm, the ordering ofthe cities, which minimizes the overall route, is selected. Thenearest neighbor algorithm is suboptimal, however, it canquickly find a near-optimal solution (in most cases) and itscomputational complexity is small (linear in the number ofcities) [25], hence making it suitable for complicatedproblems such as the task allocation problem we areconsidering. Therefore, in the proposed model, for everycoalition S, the agents can easily work out the nearestneighbor route for the tasks, and operate according to it.

Having modeled each coalition as a polling system, thepseudoconservation law in (4) allows to evaluate the cost, interms of average waiting time (or delay), from forming aparticular coalition. However, for every coalition, there is abenefit, in terms of the average effective throughput that thecoalition is able to achieve. The average effective through-put for a coalition S is given by

LS ¼Xi2S\T

�i � Pri;CR; ð6Þ

with Pri;CR given by (2). By closely inspecting (1), one cansee that adding more collectors improves the transmissionlink capacity, and, thus reduces the service time that acertain task perceives. Based on this property and by using(4), one can easily see that, adding more collectors, i.e.,improving the service time, reduces the overall delay in (4)[21], [22], [23], [24]. Further, adding more relays wouldreduce the distance over which transmission is occurring,thus, improving the probability of successful transmissionas per (2) [6], [19]. In consequence, using (6), one can seethat this improvement in the probability of successfultransmission is translated into an improvement in theeffective throughput. Hence, each agent role (collector orrelay) possesses its own benefit for a coalition.

A suitable criterion for characterizing the utility innetworks that exhibit a trade-off between the throughputand the delay is the concept of system power which isdefined as the ratio of some power of the throughput andthe delay (or a power of the delay) [26]. Hence, the conceptof power is an attractive notion that allows to capture thefundamental trade-off between throughput and delay in theproposed task allocation model. Power has been usedthoroughly in the literature in applications that are sensitiveto throughput as well as delay [27], [28], [29]. Mainly, forthe proposed game, the utility of every coalition S isevaluated using a coalitional value function based on thepower concept from [29] as follows:

vðSÞ ¼�

L�SP

i2S\T i�Wi

� �ð1��Þ ; if S < 1 and jSj > 1;

0; otherwise;

8<: ð7Þ

where � 2 ð0; 1Þ is a throughput-delay trade-off parameter.In (7), the term � represents the price per unit power that thenetwork offers to coalition S. Hence, � represents a genericcontrol parameter that allows the network operator tosomehow monitor the behavior of the players. The use ofsuch control parameters is prevalent in game theory [30],[31], [32], [33], [34]. In certain scenarios, � would represent


physical monetary values paid by the operator to thedifferent entities (agents and tasks). In such a case, on onehand, for the tasks, the operator simply would pay the tasks’owners for the amount of data (and its correspondingquality as per (7)) each one of their tasks had generated. Onthe other hand, for the agents, the payment would, forexample, represent either a reward for the behavior of theagents or the proportion of maintenance or servicing thateach agent would receiver from its operator. In this sense,the utility function in (7) would, thus, represents the totalrevenue achieved by a coalition S, given the network powerthat coalition S obtains. For coalitions that consist of a singleagent or a single task, i.e., coalitions of size 1, the utilityassigned is zero due to the fact that such coalitions generateno benefit for their member (a single agent can collect nodata unless it moves to task, while a single task cannottransmit any of its generated data without an agentcollecting these data). Further, any coalition where condi-tion (5) is not satisfied is also given a zero utility, since, inthis case, the polling system that the coalition represents isunstable, and hence has an infinite delay.

Consequently, given the set of players N , and the valuefunction given in (7), we define a coalitional game ðN ; vÞwith transferable utility (TU). The utility in (7) representsthe amount of money or revenue received by a coalition,and hence this amount can be arbitrarily apportionedbetween the coalition members, which justifies the TUnature of the game. For dividing this utility between theplayers, we adopt the equal fair allocation rule, whereby thepayoff of any player i 2 S, denoted by xSi is given by

xSi ¼vðSÞjSj : ð8Þ

The payoff xSi represents the amount of revenue thatplayer i 2 S receives from the total revenue vðSÞ that coalitionS generates. The main motivation behind adopting the equalfair allocation rule is in order to highlight the fact that theagents and the tasks value each others equally. As seen in (7),the presence of an agent in a coalition is crucial in order for thetasks to obtain any payoff, and, vice versa, the presence of atask in a coalition is required for the agent to be able to obtainany kind of utility. Nonetheless, the proposed model andalgorithm can accommodate any other type of payoffallocation rule. For instance, although in traditional coali-tional games, the allocation rule may have a strong impact onthe game’s solution, for the proposed game, other allocationrules can be used with little impact on the analysis that ispresented in the rest of the paper. This is mainly due to thenature and class of the proposed game which is quitedifferent from traditional coalitional games. In fact, as clearlyseen from (4) and (7), whenever the number of tasks in acoalition increases, the total delay increases, hence reducingthe utility from forming a coalition. Further, in a coalitionwhere the number of tasks is large, the condition of stabilityfor the polling system, as given by (5), can be easily violateddue to heavy traffic incoming from a large number of tasks,thus yielding a zero utility as per (7). Hence, formingcoalitions between the tasks and the agents entails a cost thatcan limit the size of a coalition. In this regard, traditionalsolution concepts for TU games, such as the core [20], may notbe applicable. In fact, in order for the core to exist, as asolution concept, a TU coalitional game must ensure that thegrand coalition, i.e., the coalition of all players will form.

However, as seen in Fig. 1 and corroborated by the utility in(7), in general, due to the cost for coalition formation thegrand coalition will not form. Instead, independent anddisjoint coalitions appear in the network as a result of the taskallocation process. In this regard, the proposed game isclassified as a coalition formation game [30], [31], [32], [33], [34],and the objective is to find an algorithm that allows to formthe coalition structure, instead of finding only a solutionconcept such as the core which aims mainly at stabilizing agrand coalition of all players.

4 TASK ALLOCATION AS A HEDONIC COALITION

FORMATION GAME

In this section, we map the proposed task allocationproblem to a hedonic coalition formation game with anunderlying transferable utility and we propose a distributedalgorithm for forming the coalitions using concepts fromhedonic games.

4.1 Hedonic Coalition Formation: Concepts andModel

As already mentioned, the proposed task allocation modelentails the formation of disjoint coalitions, and hence theproposed game is classified as a coalition formation game.In fact, coalition formation has been a topic of high interestin game theory [30], [31], [32], [33], [34]. Notably, in [32],[33], [34], a class of coalition formation games known ashedonic coalition formation games is investigated. This class ofgames entails several interesting properties that can beapplied, not only in economics such as in [32], [33], [34], butalso in wireless networks as we will demonstrate in thispaper. The two key requirements for classifying a coali-tional game as a hedonic game are as follows [32]:

Condition 1 (Hedonic Conditions). A coalition formationgame is classified as hedonic, if

1. The payoff of any player depends solely on themembers of the coalition to which the player belongs.

2. The coalitions form as a result of the preferences ofthe players over their possible coalitions’ set.

These two conditions characterize the framework ofhedonic games. Mainly, the term hedonic pertains to the firstcondition above, whereby the payoff of any player i, in ahedonic game, must depend only on the identity of theplayers in the coalition to which player i belongs, with nodependence on the other players. For the second condition,in the remainder of this section, we will formally definehow the preferences of the players over the coalitions can beused for the formation process.

Prior to investigating the application of hedonic games inthe proposed model, we introduce some definitions, takenfrom [32].

Definition 1. A coalition structure or a coalition partition isdefined as the set � ¼ fS1; . . . ; Slgwhich partitions the playersset N , i.e., 8 k; Sk � N are disjoint coalitions such that[lk¼1Sk ¼ N (an example of a partition � is shown in Fig. 1).

Definition 2. Given a partition � of N , for every player i 2 Nwe denote by S�ðiÞ, the coalition to which player i belongs, i.e.,coalition S�ðiÞ ¼ Sk 2 �, such that i 2 Sk.


In a hedonic game setting, each player must buildpreferences over its own set of possible coalitions. In otherwords, each player must be able to compare the coalitions,and order them based on which coalition the player prefersbeing a member of. For evaluating these preferences of theplayers over the coalitions, we define the concept of apreference relation or order as follows [32]:

Definition 3. For any player i 2 N , a preference relation ororder �i is defined as a complete, reflexive, and transitivebinary relation over the set of all coalitions that player i canpossibly form, i.e., the set fSk � N : i 2 Skg.

Consequently, for a player i 2 N given two coalitionsS1 � N and S2 � N such that i 2 S1 and i 2 S2, S1 �i S2

indicates that player i prefers to be part of coalition S1 overbeing part of coalition S2, or at least i prefers both coalitionsequally. Further, using the asymmetric counterpart of �i ,denoted by �i , then S1 �i S2 indicates that player i strictlyprefers being a member of S1 over being a member of S2.For every application, an adequate preference relation �ican be defined to allow the players to quantify theirpreferences. The preference relation can be a function ofmany parameters, such as the payoffs that the playersreceive from each coalition, the weight each player gives toother players, and so on. Given the set of players N , and apreference relation �i for every player i 2 N , a hedoniccoalition formation game is formally defined as follows [32]:

Definition 4. A hedonic coalition formation game is a coalitionalgame that satisfies the two hedonic conditions previouslymentioned, and is defined by the pair ðN ;�Þ where N is theset of players (jN j ¼ N) and� is a profile of preferences, i.e.,preference relations, ð�1; . . . ;�NÞdefined for every player inN .

Having laid out and defined the main components ofhedonic coalition formation games, we utilize this frame-work in order to provide a suitable solution for the taskallocation problem proposed in Section 2. For instance, theproposed task allocation problem is easily modeled as aðN ;�Þ hedonic game, whereN is the set of agents and taskspreviously defined and � is a profile of preferences that wewill shortly define. First and foremost, for the proposedgame model, given a network partition � of N , the payoffof any player i depends only on the identity of the membersof the coalition to which i belongs. In other words, thepayoff of any player i depends solely on the players in thecoalition in which player i belongs S�ðiÞ (easily seenthrough the formulation of Section 3). Hence, our gameverifies the first hedonic condition.

Furthermore, for modeling the task allocation problem asa hedonic coalition formation game, the preference relationsof the players must be clearly defined. In this regard, wedefine two types of preference relations, a first type suitedfor indicating the preferences of the agents, and a secondtype suited for the tasks. Subsequently, for evaluating thepreferences of any agent i 2 M, we define the followingoperation (this preference relation is common for all agents,hence we denote it by �i ¼ �M; 8i 2 M):

S2 �M S1 , uiðS2Þ � uiðS1Þ; ð9Þ

where S1 � N and S2 � N are any two coalitions thatcontain agent i, i.e., i 2 S1 and i 2 S2 and ui : 2N ! IR is apreference function defined for any agent i as follows:

uiðSÞ ¼1; if S ¼ S�ðiÞ & S n fig � T ;0; if S 2 hðiÞ;xSi : otherwise;

8<: ð10Þ

where � is the current coalition partition which is in place inthe game, xSi is the payoff received by player i from anydivision of the value function among the players in coalitionS such as the equal fair division given in (8), and hðiÞ is thehistory set of player i. At any point in time, the history sethðiÞ is a set that contains the coalitions that player iwas a partof in the past, prior to the formation of the current partition�. Note that, by using the defined preference relation, theplayers can compare any two coalitions S1 and S2 indepen-dently of whether these two coalitions belong to � or not.

The main rationale behind the preference function ui in(10) is as follows: In this model, the agents, being entitiesowned by the operator, seek out to achieve two conflictingobjectives: 1) Service all tasks in the network for the benefit ofthe operator and 2) Maximize the quality of service, in termsof power as per (7), for extracting the data from the tasks. Thepreference function ui must be able to allow the agents tomake coalition formation decisions that can capture thistrade-off between servicing all tasks (at the benefit of theoperator) and achieving a good quality of service (at thebenefit of both agents and operator). For this purpose, as per(10), any agent i that is the sole agent servicing tasks in itscurrent coalition S ¼ S�ðiÞ such that S�ðiÞ \M ¼ fig,assigns an infinite preference value to S. Hence, in order toservice all tasks, the agent always assigns a maximumpreference to its current coalition, if this current coalition iscomposed of only tasks and does not contain other agents.This case of the preference function ui forbids the agent fromleaving a group of tasks, already assigned to it, unattendedby other agents. In this context, this condition pertains to thefirst objective (objective 1 previously mentioned) of theagents and it implies that, whenever there is a risk of leavingtasks without service, the agent do not act selfishly, incontrast, they act in the benefit of the operator and remainwith these tasks, independent of the payoff generated bythese tasks. Such a decision allows an agent to avoid makinga decision that can incur a risk of ultimately having taskswith no service in the network, in which case, the networkoperator would lose revenue from these unattended tasksand it may, for example, decide to replace the agent that ledto the presence of such a group of tasks with no service.Otherwise, the agents’ preference relation ui would highlightthe second objective of the agent, i.e., maximize its ownpayoff which maps into the revenue generated from thequality of service, i.e., the power as per (7), with which thetasks are being serviced. In this case, the preference relationis easily generated by the agents by comparing the value ofthe payoffs they receive from the two coalitions S1 and S2.Further, we note that no agent has any incentive to revisit acoalition that it had left previously, and hence the agentsassign a preference value of 0 for any coalition in theirhistory (this can be seen as a basic learning process). Insummary, taking into account the conflicting goals of theagents between two coalitions S1 and S2, an agent i prefersthe coalition that gives the better payoff, given that the agentis not alone in its current coalition, and the coalition with abetter payoff is not in the history of agent i.

For the preferences of the tasks, an analogous approachcan be taken. Formally, for evaluating the preferences ofany task j 2 T , we define the following operation (this


preference relation is common for all tasks, hence we denoteit by �j ¼ �T ; 8j 2 T ):

S2 �T S1 , wjðS2Þ � wjðS1Þ; ð11Þ

with the tasks’ preference function wj defined as follows:

wjðSÞ ¼0; if S 2 hðjÞ;xSj ; otherwise:

�ð12Þ

The preferences of the tasks are easily captured using thefunction wj. The preference function of the tasks is differentfrom that of the agents since the tasks are, in general,independent entities that act solely in their own interest.Thus, based on (12), each task prefers the coalition thatprovides the larger payoff xSj unless this coalition wasalready visited previously and left. In that case, thepreference function of the tasks assigns a preference valueof 0 for any coalition that the task had already visited inthe past (and left to join another coalition). Using thispreference relation, every task can evaluate its preferencesover the possible coalitions that the task can form.

Consequently, the proposed task allocation modelverifies both hedonic conditions, and hence we have thefollowing:

Property 4. The proposed task allocation problem among theagents is modeled as a ðN ;�Þ hedonic coalition formationgame, with the preference relations given by (9) and (11).

Note that the preference relations in (9) and (11) are alsodependent on the underlying TU coalitional game describedin Section 3. Having formulated the problem as a hedonicgame, the final task is to provide a distributed algorithmbased on the defined preferences for forming the coalitions.

Prior to deriving the algorithm for coalition formation,we highlight the following proposition of the proposedhedonic coalition formation model as a result of the pollingsystem stability indicated in (5):

Proposition 1. For the proposed hedonic coalition formationmodel for task allocation, assuming that all collector-agentshave an equal link transmission capacity �i ¼ �; 8i 2 M, anycoalition S � N with jS \Mj agents, must have at leastjGSjmin collector-agents (GS � S \M) as follows:

jGSj > jGSjmin ¼P

i2S\T �i�

: ð13Þ

Further, when all the tasks in S belong to the same class, we have

jGSjmin ¼jS \ T j � �

�; ð14Þ

which constitutes an upper bound on the number of collector-agents as a function of the number of tasks jS \ T j for a givencoalition S.

Proof. As per the defined preference relations in (10) and(12), any coalition that will form in the proposed modelmust be stable since no agent or task has an incentive tojoin an unstable coalition, hence, we have for everycoalition S � N having jGSj collectors with GS � S \M,we have from (5) S < 1, and thus

Xi2S\T

�i�GS

< 1;

which given the assumption that �i ¼ �; 8i 2 M yields

1

jGSj � ��Xi2S\T

�i < 1;

which yields

jGSj > jGSjmin ¼P

i2S\T �i�

: ð15Þ

Further, if we assume that all the tasks belong to thesame class, hence, �i ¼ �; 8i 2 S \ T , we immediatelyget, from (15),

jGSjmin ¼jS \ T j � �

�: ð16Þ

tu

Consequently, for any proposed coalition formationalgorithm, the bounds on the number of collector-agentsin any coalition S as given by Proposition 1 will alwaysbe satisfied.

4.2 Hedonic Coalition Formation: Algorithm

In the previous section, we modeled the task allocationproblem as a hedonic coalition formation game. Having laidout the main building blocks, the remaining objective is todevise an algorithm for forming the coalitions. Whileliterature that studies the characteristics of existing parti-tions in hedonic games such as in [32], [33], [34] isabundant, the problem of forming the coalitions both inthe hedonic and nonhedonic setting is a challengingproblem [30]. In this paper, we introduce an algorithm forcoalition formation that allows the players to make selfishdecisions as to which coalitions they decide to join at anypoint in time. The proposed algorithm will exploit theconcepts of the hedonic game model formulated in theprevious section.

In this regard, for forming coalitions between the tasksand the agents, we propose the following rule for coalitionformation:

Definition 5 (Switch Rule). Given a partition � ¼fS1; . . . ; Slg of the set of players (agents and tasks) N , aPlayer i decides to leave its current coalition S�ðiÞ ¼ Sm, forsome m 2 f1; . . . ; lg and join another coalition Sk 2 � [f;g; Sk 6¼ S�ðiÞ, if and only if Sk [ fig �i S�ðiÞ. Hence,fSm; Skg ! fSm n fig; Sk [ figg.

Through a single switch rule made by any player i, anycurrent partition � of N is transformed into �0 ¼ ð� n fSm;SkgÞ [ fSm n fig; Sk [ figg. In simple terms, for every parti-tion �, the switch rule provides a mechanism throughwhich any task or agent can leave its current coalition S�ðiÞ,and join another coalition Sk 2 �, given that the newcoalition Sk [ fig is strictly preferred over S�ðiÞ throughany preference relation that i is using (in particular, usingthe preference relations defined in (9) and (11)). Indepen-dent of the preference relations selected, the switch rule canbe seen as a selfish decision made by a player to move fromits current coalition to a new coalition regardless of theeffect of this move on the other players. Furthermore, weconsider that whenever a player decides to switch from one


coalition to another, the player updates its history set hðiÞ.Hence, given a partition �, whenever a player i decides toleave coalition Sm 2 � to join a different coalition, coalitionSm is automatically stored by player i in its history set hðiÞ.

Consequently, we propose a coalition formation algo-rithm composed of three main phases: Task discovery,hedonic coalition formation, and data collection. In the firstphase, the central command receives information about theexistence of tasks that require servicing and informs theagents of the locations and characteristics of the tasks (e.g.,the arrival rates). Hence, the agents start by having fullknowledge of the initial partition �initial. Once the agents areaware of the tasks, they broadcast their own presence to thetasks. Consequently, the players can interact with eachother for performing coalition formation. Hence, the secondphase of the algorithm is the hedonic coalition formationphase. In this phase, all the players (tasks and agents)investigate the possibility of performing a switch operation.For identifying potential switch operations, given completeknowledge about the network (which can be gathered indifferent methods as will be discussed in Section 4.3)), eachagent investigates its top preference and decides to performa switch operation if possible through (9). As one can easilysee through (7), in the proposed model, no coalitioncomposed of tasks-only would ever form since such acoalition would always generate a zero utility. As a directresult of this property, the tasks are only interested inswitching to coalitions that contain at least a single agent.Hence, from a tasks’ perspective for determining itspreferred switch operation, each task needs only tonegotiate with existing agents in order to enquire on theamount of utility it can obtain by joining with this agent. Bydoing so, each task can determine the switch operation it isinterested in making at a given time. We consider that theplayers make sequential switch decisions.7 For any agent, aswitch operation is easily performed as the agent can leaveits current coalition and join the new coalition if (9) issatisfied. For the tasks, any task that finds out a possibilityto switch can autonomously request over a control channelwith the concerned agent to be added to the coalition ofinterest (which would always contain at least one agentwith whom the task previously negotiated). The conver-gence of the proposed hedonic coalition formation algo-rithm during this phase is guaranteed as follows:

Theorem 1. Starting from any initial network partition �initial,the proposed hedonic coalition formation phase of the proposedalgorithm always converges to a final network partition �f

composed of a number of disjoint coalitions.

Proof. For the purpose of this proof, we denote �knk

as thepartition formed during the time k when player i 2 Ndecides to act after nk switch operations have previouslyoccurred (the index nk denotes the number of switchoperations performed by one or more players up totime k). Given any initial starting partition �initial ¼ �1

0,the hedonic coalition formation phase of the proposedalgorithm consists of a sequence of switch operations. Asper Definition 5, every switch operation transforms thecurrent partition � into another partition �0, hence thehedonic coalition formation is composed of a sequence of

switch operations, yielding the following transforma-tions (as an example):

�10 ¼ �2

0 ! �31 ! � � � ! �L

nL� � � ! � � � ! �T

nT; ð17Þ

where the operator! indicate the occurrence of a switchoperation. In other words, �k

nk! �kþ1

nkþ1, implies that

during turn k, a certain player i made a single switchoperation which yielded a new partition �kþ1

nkþ1at the turn

kþ 1. By inspecting the preference relations defined in(9) and (11), it can be seen that every single switchoperation leads to a partition that has not yet been visited(new partition). Hence, for any two partitions �k

nkand

�lnl

in the transformations of (17), such that nk 6¼ nl,i.e., �l

nlis a result of the transformation of �k

nk(or vice

versa) after a number of switch operations jnl � nkj, wehave that �k

nk6¼ �l

nlfor any two turns k and l.

Given this property and the well-known fact that thenumber of partitions of a set is finite and given by the Bellnumber [30], the number of transformations in (17) isfinite, and hence the sequence in (17) will always terminateand converge to a final partition �f ¼ �T

nT. Hence, the

hedonic coalition formation phase of the proposedalgorithm always converges to a final network partition�f composed of a number of disjoint coalitions consistingof agents and tasks, which completes the proof. tu

The stability of the final partition �f resulting from theconvergence of the proposed algorithm can be studied usingthe following stability concept from hedonic games [32]:

Definition 6. A partition � ¼ fS1; . . . ; Slg is Nash-stable if8i 2 N ; S�ðiÞ �i Sk [ fig for all Sk 2 � [ f;g (for agents�i¼�M; 8i 2 N \M and for tasks �i¼�T ; 8i 2 N \ T ).

In other words, a coalition partition � is Nash-stable, ifno player has an incentive to move from its current coalitionto another coalition in � or to deviate and act alone.Furthermore, a Nash-stable partition � implies that theredoes not exist any coalition Sk 2 N such that a player istrictly prefers to be part of Sk over being part of its currentcoalitions, while all players of Sk do not get hurt by formingSk [ fig. This is the concept of individual stability, which isformally defined as follows [32]:

Definition 7. A partition � ¼ fS1; . . . ; Slg is individuallystable if there do not exist i 2 N , and a coalition Sk 2� [ f;g such that Sk [ fig �i S�ðiÞ and Sk [ fig �j Sk forall j 2 Sk (for agents �i¼�M; 8i 2 N \M and for tasks �i¼�T ; 8i 2 N \ T for tasks).

As already noted, a Nash-stable partition is individuallystable [32]. For the proposed hedonic coalition formationphase of the proposed algorithm, we have the following:

Proposition 2. Any partition �f resulting from the hedoniccoalition formation phase of the proposed algorithm is Nash-stable, and hence individually stable.

Proof. First and foremost, for any partition �, no player(agent or task) i 2 N has an incentive to leave its currentcoalition, and act alone as per the utility function in (7).Assume that the partition �f resulting from the proposedalgorithm is not Nash-stable. Consequently, there exists a


7. This order of switch operations is referred to as the order of playhereafter.

player i 2 N , and a coalition Sk 2 �f such that Sk [fig �i S�f

ðiÞ, hence, player i can perform a switchoperation which contradicts with the fact that �f is theresult of the convergence of the proposed algorithm(Theorem 1). Consequently, any partition �f resultingfrom the hedonic coalition formation phase of theproposed algorithm is Nash-stable, and hence by [32],this resulting partition is also individually stable. tu

Following the formation of the coalitions and theconvergence of the hedonic coalition formation phase to aNash-stable partition, the last phase of the algorithm entailsthe actual data collection by the agents. In this phase, theagents move from one task to the other, in their respectivecoalitions, collecting the data and transmitting it to thecentral receiver, similar to a polling system, as explained inSections 2 and 3. A summary of the proposed algorithm isshown in Table 1.

The proposed algorithm, as highlighted in Table 1, canadapt the network topology to environmental changes, suchas the deployment of new tasks, the removal of a number ofexisting tasks, or a periodic low mobility of the tasks (in thecase where the tasks represent mobile sensor devices forexample). For this purpose, the first two phases of thealgorithm shown in Table 1 are repeated periodically overtime, to adapt to any changes that occurred in theenvironment. With regards to mobility, we only considerthe cases where the tasks are mobile for a fixed period of timewith a velocity that is smaller than that of the agents �. In thepresence of such a mobile environment, the central com-mand center, through Phase I of the algorithm in Table 1informs the agents of the new tasks locations (periodically)and, thus, during Phase II of the proposed algorithm, bothagents and tasks can react to the environment changes, andmodify the existing topology. As per Theorem 1 andProposition 2, regardless of the starting position, the playerswill always self-organize into a Nash-stable partition, evenafter mobility, the deployment of new tasks or the removal ofexisting tasks. In summary, in a changing environment, thefirst two phases of the algorithm in Table 1 are repeatedperiodically, after a certain fixed period of time � has elapsedduring which the players were involved in Phase III and theactual data collection and transmission occurred. Finally,whenever a changing environment is considered, the playersare also allowed to periodically clear their history, so as toallow them to explore all the new possibilities that thechanges in the environment may have yielded.

4.3 Distributed Implementation Possibilities

For implementation, first and foremost, in the proposedmodel, as shown in Fig. 1, we clearly distinguish betweentwo inherently different entities: The command center,which is the intelligence that has some control over theagents and the central receiver which is a node in thenetwork that is connected to the command center andwhich would receive the data transmitted by the agents(this distinction can be, for example, analogous to thedistinction between a radio network controller and a basestation in cellular networks). In practice, the centralcommand can be, for example, a node that owns a numberof agents and controls a large area which is divided into

smaller areas with each area represented by the illustrationof Fig. 1. Hence, each such small area is a region having itsown central receiver and where a subset of agents needs tooperate and perform coalition formation using our model.In other scenarios, the command center can also be asatellite system that controls groups of agents with eachgroup deployed in a different area (notably when the agentsare unmanned aerial vehicles for example). In contrast, thecentral receiver is simply a wireless node that receives thedata from the agents and, subsequently, the commandcenter can obtain these data from all receivers in itscontrolled area (e.g., through a backbone network).8

For performing coalition formation, the agents and tasksare required to know different information. From the agentsperspective, in order to perform a switch operation, eachagent is required to obtain data on the location of the tasks(hence, consequently deducing the hop distanceDij betweenany two tasks i and j) as well as on the arrival rates �i; i 2 Tof these tasks. As a first step, whenever a tasks’ owner (e.g., aservice provider or a third party) requires that its tasks beserviced, it will give the details and characteristics of thesetasks to the network operator (through service-level agree-ments for example) which would enter these details into thecommand center. Subsequently, the command center caninsert this information into appropriate databases that theagents can access through, for example, an Internet connec-tion. Such a transfer of information through active databaseshas been recently utilized in many communication archi-tectures, for example, in cognitive radio network for primaryuser information distribution [35] or in unmanned aerialvehicles operation [36], [37]. In cases where the commandcenter controls only a single set of agents and a single area,this information can be, instead, broadcast directly to theagents. Further, the agents are also required to know thecapabilities of each others, notably, the link transmissioncapacity �i; 8i 2 M and the velocity (which can be used todeduce the switchover times). As the agents are all owned bya single operator, this information can be easily fed to theagents at the beginning of all time prior to their deployment,and thus does not require any additional communicationduring coalition formation.

From the tasks perspective, the amount of informationthat needs to be known is much less than that of the agents,notably since the tasks are, in general, resource-limitedentities. For instance, as mentioned in the previous section,for performing coalition formation, the tasks do not need toknow about the existence or the characteristics of eachothers. The main information that needs to be known by thetasks is the actual presence of agents. The agents caninitially announce/broadcast their presence to the tasks assoon as they enter into the network. Subsequently, the tasksneed only to be able to enquire, over a control channel,about the potential utility they would receive from joiningthe coalition of a particular agent (which can contain othertasks or agents but this is transparent from the perspectiveof the tasks). The main reason for this is that the taskshave no benefit in forming coalitions that have no agentssince such coalitions generate zero utility for the tasks.Hence, from the point of view of the tasks, they would seeevery agent as a black box which can provide a certain


8. This model can easily accommodate the particular case where thecommand center and the central receiver coincide, e.g., in a small single-area network.

payoff (communicated over a control channel duringnegotiation phase), and based on this, they decide to jointhe coalition one or another agent (if multiple agents are inthe same coalition then they would offer the same benefit

from the tasks perspective). Note that, for coalitions thatcontain multiple agents, the task needs only to ask one agentabout their potential utility. In fact, this agent can append,along with the information on the utility, a signal to the


TABLE 1The Proposed Hedonic Coalition Formation Algorithm for Task Allocation in Wireless Networks

tasks about other agents that belong to the same coalition.By doing so, the tasks would no longer need to assesswhether to join a coalition by enquiring from other agentsthat belong to the same coalition, i.e., having redundantinformation. Hence, by sending this additional information,the agent will enable the tasks to avoid doing multipleprocessing for the same enquiry.

Consequently, given the information that needs to beknown by each player, the proposed algorithm can beimplemented in a distributed way since the switchoperation can be performed by the tasks or the agentsindependently of any centralized entity. In this regard,given a partition �, in order to determine its preferredswitch operation, an agent would assess the payoff it wouldobtain by joining with any coalition in �, except forsingleton coalitions composed of agents only. For the tasks,given �, each task negotiates with only the agents (and thecoalition to which they belong) in the network in order toevaluate its payoff and decide on a switch operation. Byadopting a distributed implementation, one would reducethe overhead and computational load on the commandcenter, notably when this command center is controllingnumerous areas with different groups of agents (each sucharea is represented by the model of Fig. 1). Further, thedistributed approach allows to decentralize the intelligence,and, thus, reduces the detrimental effects on the networkand the tasks’ owners that can be caused by failures ormalicious behavior at the command center level. It is alsoimportant to note that the distributed approach compliesbetter with the nature of both the agents and the tasks. Onone hand, the agents are inherently autonomous nodes(partially controlled by the command center) that need tooperate on their own and, thus, make distributed decisions[1], [2], [3], [6], [7], [8]. On the other hand, the tasks areindependent entities that belong to different owners.Consequently, the tasks are apt to make their own decisionsregarding coalition formation and are, generally, unwillingto accept a coalitional structure imposed by an externalentity, such as the command center. Nonetheless, we notethat a centralized approach can also be adopted for theproposed algorithm notably in small networks where, forexample, the command center coincides with the centralreceiver and owns all the tasks.

Regarding complexity, the main complexity lies in theswitch operation, the solution to the traveling salesmanproblem, i.e., determining the order in which the tasks arevisited within a coalition in order to evaluate the utilityfunction, and the assignment of agents as either collectors orrelays. For instance, given a present coalitional structure �where each coalition in � has at least one task, for everyagent, the computational complexity of finding its nextcoalition, i.e., performing a switch operation, is easily seento be Oðj�jÞ, and the worst-case scenario is when all thetasks act alone, in that case j�j ¼ T . In contrast, for thetasks, the worst-case complexity is OðMÞ since, in order tomake a switch operation, the tasks need only to negotiatewith agents. With regards to the traveling salesmansolution, the complexity of the used nearest neighborsolution is well known to be linear in the number of cities,i.e., tasks [25], hence for a coalition Sk 2 �, the complexityof finding the traveling salesman solution is simplyOðjSk \ T jÞ, where Sk \ T is the set of tasks inside coalitionSk. During coalition formation, i.e., Phase II of the

algorithm, whenever a coalition Sk is formed, this coalitionneeds to compute its own traveling salesman problem,which has a linear complexity OðjSk \ T jÞ, as alreadymentioned. Certainly, the overall number of travelingsalesman problems that should be solved also depends onthe number of new coalitions that were potentially evalu-ated for coalition formation prior to convergence to theNash-stable partition. Hence, the number of travelingsalesman solutions that need to be computed is propor-tional to the number of coalitions (and the identity andnumber of the tasks within) that negotiated a potentialcoalition formation prior to convergence. This certainlydepends on the number of iterations till convergence andthe number of switch operations that occurred. None-theless, for static environments, after coalition formation ends,i.e., in Phase III of the algorithm in Table 1, the travelingsalesman solution needs to be computed only once for eachcoalition and, afterwards, the network can operate indefi-nitely (if the environment is static) without any need for thecoalitions to recompute the traveling salesman solution.

Additionally, for determining whether an agent acts as acollector or relay within any coalition, we consider that theplayers would compute this configuration by inspecting allcombinations and selecting the one that maximizes theutility in (7). This computation is done during coalitionformation for evaluating the potential utility, and, uponconvergence, is maintained during network operation. Asthe number of agents in a single coalition is generally small,this computation is straightforward, and has reasonablecomplexity. Finally, in dynamic environments, as thealgorithm is repeated periodically and since we consideronly periodic low mobility, the complexity of the coalitionformation algorithm is comparable to the one in the staticenvironment, but with more runs of the algorithm.

5 SIMULATION RESULTS AND ANALYSIS

For simulations, the following network is set up: A centralreceiver is placed at the origin of a 4� 4 km square area withthe tasks appearing in the area around it. The path lossparameters are set to � ¼ 3 and � ¼ 1, the target SNR is set to�0 ¼ 10 dB, the pricing factor is set to � ¼ 1, and the noisevariance �2 ¼ �120 dBm. All packets are considered of size256 bits which is a typical IP packet size. The agents areconsidered as having a constant velocity of � ¼ 60 km/h, atransmit power of ~P ¼ 100 mW, and a transmission linkcapacity of � ¼ 768 kbps (assumed the same for all agents).Further, we consider two classes of tasks in the network. Afirst class that can be mapped to voice services having anarrival rate of 32 kbps, and a second class that can be mappedto video services, such as the widely known QuarterCommon Intermediate Format (QCIF) [38], having an arrivalrate 128 kbps. Tasks belonging to each class are generatedwith equal probability in the simulations. Unless statedotherwise, the throughput-delay trade-off parameter � is setto 0.7 to indicate services that are reasonably delay tolerant.

In Fig. 2, we show a snapshot of the final networkpartition reached through the proposed hedonic coalitionformation algorithm for a network consisting of M ¼ 5agents and T ¼ 10 arbitrarily located tasks. In this figure,Tasks 1, 3, and 8 belong to the QCIF video class with anarrival rate of 128 kbps, while the remaining tasks belongto the voice class with an arrival rate of 32 kbps. In Fig. 2,


we can easily see how the agents and tasks can agree on apartition whereby a number of agents service a group ofnearby tasks for data collection and transmission. For thenetwork of Fig. 2, the tasks are distributed into threecoalitions, two of which (coalitions S1 and S3) are servedby a single collector-agent. In contrast, coalition S2 isserved by two collectors and one relay. The agents incoalition 2 distributed their roles (relay or collector)depending on the achieved utility. For instance, forcoalition S2, having two collectors and one relay providesa utility of vðS2Þ ¼ 52:25, while having three collectorsyields a utility of vðS2Þ ¼ 10:59, and having one collectorand two relays yields a utility of vðS2Þ ¼ 45:19. As a result,the case of two collectors and one relay maximizes theutility and is agreed upon between the players. Further, thecoalitions in Fig. 2 are dynamic, in the sense that withineach coalition the agents move from one task to the other,collecting and transmitting data to the receiver continu-ously. The order in which the agents visit the tasks, asindicated in Fig. 2, is generated using a nearest neighborsolution for the traveling salesman problem as given byProperty 3. For example, consider coalition S2 in Fig. 2. Inthis coalition, agents 3 and 5 act as a single collector andmove from task 1 to task 3 to task 10, and then back totask 1 repeating these visits in a cyclic manner. Concur-rently with the collectors movement, agent 2 of coalitionS2, moves and positions itself at the middle of the lineconnecting the task being serviced by agents 3 and 5 tothe central receiver. In other words, when the collectors areservicing task 1, agent 2 is at the middle of the lineconnecting task 1 to the central receiver, subsequentlywhen the collectors are servicing task 3, agent 2 takesposition at the middle of the line connecting task 3 to thecentral receiver, and so on. Finally, note that for all thecoalitions in Fig. 2, one can verify that the minimumnumber of collectors, as per Proposition 1, is approximatelyone, (e.g., for coalition S2, we have jGS2

jmin ¼ 924 thus one

collector is a minimum), and hence this condition is easilysatisfied by the coalition formation process.

In Fig. 3, we assess the performance of the proposedhedonic coalition formation algorithm, in terms of the payoff(revenue) per player (agent or task) for a network havingM ¼ 5 agents, as the number of tasks increases. The figureshows the statistics (averaged over the random positions ofthe tasks), in terms of maximum, average, and minimumover the random order of play. In this figure, we comparethe performance with an algorithm that assigns the tasksequally among the agents (i.e., an equal group of neighbor-ing tasks are assigned for every agent). Fig. 3 shows that theperformance of both algorithms is bound to decrease as thenumber of tasks increases. This is mainly due to the fact that,for networks having a larger number of tasks, the delayincurred per coalition, and, thus, per user increases. Thisincrease in the delay is not only due to the increase in thenumber of tasks, but also to the increase in the distance thatthe agents need to travel within their correspondingcoalitions (increase in switchover times). In Fig. 3, we notethat the minimum payoff achieved by the proposedalgorithm is comparable to that of the equal allocation.Hence, the performance of the proposed algorithm is clearlylower bounded by the equal allocation algorithm. However,Fig. 3 shows that the average and maximum payoff resultingby the proposed algorithm is significantly better than theequal allocation at all network sizes up to T ¼ 25 tasks.Albeit this performance improvement decreases with theincrease in the number of tasks, the performance, in terms ofaverage payoff per player, yielded by the proposedalgorithm is no less than 30.26 percent better than the equalallocation for up to T ¼ 25 tasks. Beyond T ¼ 25 tasks, Fig. 3shows that the average and maximum performance of theproposed algorithm is comparable to that of the equalallocation, notably at T ¼ 40 tasks. The reduction in theperformance gap between the two algorithms for largenetworks stems from the fact that, as more tasks exist in thenetwork, for a fixed number of agents, the possibility of


Fig. 2. A snapshot of a final coalition structure resulting from theproposed hedonic coalition formation algorithm for a network of M ¼ 5agents and T ¼ 10 tasks. In every coalition, the agents (collectors andrelays) visit the tasks continuously in the shown order.

Fig. 3. Performance statistics, in terms of maximum, average, andminimum (over the order of play) player payoff (revenue), of theproposed hedonic coalition formation algorithm compared to analgorithm that allocates the neighboring tasks equally among the agentsas the number of tasks increases for M ¼ 5 agents. All the statistics arealso averaged over the random positions of the tasks.

forming large coalitions, through the proposed hedoniccoalition formation algorithm is reduced, and hence thestructure becomes closer to equal allocation.

In Fig. 4, we show the statistics (averaged over therandom positions of the tasks), in terms of maximum,average, and minimum (over the random order of play)payoff per player for a network with T ¼ 20 tasks as thenumber of agents M increases. The performance is onceagain compared with an algorithm that assigns the tasksequally among the agents (i.e., an equal group of neighbor-ing tasks are assigned for every agent). Fig. 4 shows that theperformance of both algorithms increases as the number ofagents increases. This is mainly due to the fact that whenmore agents are deployed, the tasks can be better servicedas the delay incurred per coalition decreases and theprobability of successful transmission improves. For in-stance, as more agents enter the network, they can act aseither collectors (for improving the delay) or relays (forimproving the success probability). We note that, at M ¼ 3,the performance statistics of the proposed algorithmconverge to the equal allocation algorithm since, for a smallnumber of agents, the flexibility of forming coalitions isquite restricted and equal allocation is the most straightfor-ward coalitional structure. Nonetheless, Fig. 4 shows that,as M increases, the performance of the proposed algorithm,in terms of maximum and average payoff achieved,becomes significantly larger than that of the equal allocationalgorithm, and this performance advantage increases asmore agents are deployed. Finally, Fig. 4 also shows that theminimum performance of the proposed algorithm iscomparable to the equal allocation algorithm for networkwith a small number of agents, but as the number of agentsincreases, the minimum performance of hedonic coalitionformation is 29 percent better than the equal allocation caseat M ¼ 7 and this advantage increases further with M.

In Fig. 5, we show the average and maximum (over therandom order of play) coalition size resulting from theproposed algorithm as the number of tasks T increases, for a

network of M ¼ 5 agents and arbitrarily deployed tasks.These results are averaged over the random positions of thetasks and are compared with the equal allocation algorithm.In this figure, we note that as the number of tasks increases,the average coalition size for both algorithms increases. Forthe proposed algorithm, the maximum coalition size alsoincreases with the number of tasks. This is an immediateresult of the fact that, as the number of tasks increases, theprobability of forming larger coalitions is higher and, hence,our proposed algorithm yields larger coalitions. Further, atall network sizes, the proposed algorithm yields coalitionsthat are relatively larger than the equal allocation algorithm.This result implies that, by allowing the players (agentsand tasks) to selfishly select their coalitions, through theproposed algorithm, the players have an incentive tostructure themselves in coalitions with average size lowerbounded by the equal allocation. In a nutshell, throughhedonic coalition formation, the resulting topology mainlyconsists of networks composed of a large number of smallcoalitions as demonstrated by the average coalition size.However, in a limited number of cases, the network topologycan also be composed of a small number of large coalitions ashighlighted by the maximum coalition size shown in Fig. 5.

In Fig. 6, we show, over a period of 5 minutes, thefrequency in terms of average switch operations per minuteper player (agent or task) achieved for various velocities ofthe tasks in a mobile wireless network with M ¼ 5 agentsand different number of tasks. As the velocity of the tasksincreases, the frequency of the switch operations increasesfor both T ¼ 10 and T ¼ 20 due to the changes in thepositions of the various tasks incurred by mobility. Fig. 6shows that the case of T ¼ 20 tasks yields a frequency ofswitch operations significantly higher than the case of T ¼10 tasks. This result is interpreted by the fact that, as thenumber of tasks increases, the possibility of finding newpartners as the tasks move increases significantly, henceyielding an increase in the topology variation as reflected bythe number of switch operations. In summary, this figure


Fig. 4. Performance statistics, in terms of maximum, average, andminimum (over the order of play) player payoff (revenue), of theproposed hedonic coalition formation algorithm compared to analgorithm that allocates the neighboring tasks equally among the agentsas the number of agents increases for T ¼ 20 tasks. All the statistics arealso averaged over the random positions of the tasks.

Fig. 5. Average and maximum (over order of play) coalition size yieldedby the proposed hedonic coalition formation algorithm and an algorithmthat allocates the neighboring tasks equally among the agents, as afunction of the number of tasks T for a network of M ¼ 5 agents. Thesestatistics are also averaged over random positions of the tasks.

shows that the proposed hedonic coalition formationalgorithm allows the agents and the tasks to self-organizeand adapt their topology to mobility, through adequateswitch operations.

The network’s adaptation to mobility is further assessedin Fig. 7, where we show, over a period of 5 minutes, theaverage coalition life span (in seconds) achieved for variousvelocities of the tasks in a mobile wireless network withM ¼ 5 agents and different number of tasks. The coalitionlife span is defined as the time (in seconds) during which acoalition is present in the mobile network prior to acceptingnew members or breaking into smaller coalitions (due toswitch operations). In this figure, we can see that, as thevelocity of the tasks increases, the average life span of acoalition decreases. This is due to the fact that, as mobilityincreases, the possibility of forming new coalitions orsplitting existing coalitions increases significantly. Forexample, for T ¼ 20, the coalition life span drops fromaround 124 seconds for a tasks’ velocity of 10 km/h to justunder a minute as of 30 km/h, and down to around42 seconds at 50 km/h. Furthermore, Fig. 7 shows that asmore tasks are present in the network, the coalition life spandecreases. For instance, for any given velocity, the life spanof a coalition for a network with T ¼ 10 tasks is significantlylarger than that of a coalition in a network with T ¼ 20 tasks.This is a direct result of the fact that, for a given tasks’velocity, as more tasks are present in the network, theplayers are able to find more partners to join with, and hencethe life span of the coalitions becomes shorter. In brief, Fig. 7provides an interesting assessment of the topology adapta-tion aspect of the proposed algorithm through the process offorming new coalitions or breaking existing coalitions.

Moreover, for further analysis of the self-adapting aspectof the proposed hedonic coalition formation algorithm, westudy the variations of the coalitional structure over time fora network where tasks are entering and leaving the network.For this purpose, in Fig. 8, we show the variations of theaverage (over the random positions of the tasks) number ofplayers per coalition, i.e., the average coalition size, over a

period of 10 minutes, as new tasks join the network and/orexisting tasks leave the network. The considered network inFig. 8 possesses M ¼ 5 agents and starts with T ¼ 15 tasks.The results are shown for different rates of change which isdefined as the number of tasks that have either entered thenetwork or left the network per minute. For example, a rateof change of two tasks per minute indicates that either twotasks enter the network every minute, two tasks leave thenetwork every minute, or one task enters the network andanother task leaves the network every minute (these casesmay occur with equal probability). In this figure, we can seethat, as time evolves, the structure of the network ischanging with new coalitions forming and other breaking


Fig. 6. Frequency of switch operations per minute per player (agent ortask) achieved over a period of 5 minutes for different tasks’ velocities inwireless network having M ¼ 5 agents and different number of mobiletasks.

Fig. 7. Average coalition life span (in seconds) achieved over a period of5 minutes for different tasks’ velocities in wireless network having M ¼ 5agents and different number of mobile tasks. The coalition life spanindicates the time during which a coalition is present in the networkbefore accepting new partners or breaking into smaller coalitions (due toswitch operations).

Fig. 8. Topology variation over time as new tasks join the network andexisting tasks leave the network with different rates of tasks arrival/departure for a network starting with T ¼ 15 tasks and having M ¼ 5agents.

as reflected by the change in coalitions size. Furthermore,we note that, as the rate of change increases, the changes inthe topology increase. For instance, it is seen in Fig. 8 thatfor a rate of change of five tasks per minute, the variations inthe coalition size are much larger than for the case of twotasks per minute (which is almost constant for many periodsof time). In summary, Fig. 8 shows the network topologyvariations as tasks enter or leave the network. Note that,after the 10 minutes have elapsed, the network reenters inthe Phase III of the algorithm where data collection andtransmission occurs.

In Fig. 9, we assess the performance of the proposedhedonic coalition formation algorithm, in terms of the payoff(revenue) per player (agent or task) for a network havingM ¼ 5 agents and T ¼ 20 tasks, as the throughput-delaytrade-off parameter � increases. The figure shows thestatistics, in terms of maximum, average, and minimumover the random order of play between the players. In thisfigure, we can see that, for small �, the performance of theproposed algorithm is comparable to the equal allocationalgorithm and the payoffs are generally small. This result isdue to the fact that, for small �, the tasks are highly delay-sensitive, and the delay component of the utility governs theperformance. Hence, for such tasks, the proposed algorithmyields a performance similar to equal allocation. However, asthe trade-off parameter � increases, the maximum andaverage utility yielded by our proposed algorithm outper-forms the equal allocation algorithm significantly. Forinstance, as of � ¼ 0:5, hedonic coalition formation is highlydesirable and presents a performance improvement in termsof average payoff of around 19.56 percent relative to theequal allocation algorithm (at � ¼ 0:55, the proposedalgorithm has an average payoff of 0.55 while equalallocation has an average payoff of 0.46). This advantageincreases with �. Note that, for all trade-off parameters,the performance of the proposed algorithm, in terms of

minimum (over order of play) payoff gained by a player islower bounded by the equal allocation algorithm and, inaverage, outperforms the equal allocation algorithm.

6 CONCLUSIONS

In this paper, we introduced a novel model for task allocationamong a number of autonomous agents in a wirelesscommunication network. In the introduced model, a numberof wireless agents are required to service several tasks,arbitrarily located in a given area. Each task represents aqueue of packets that require collection and wirelesstransmission to a centralized receiver by the agents. Thetask allocation problem is modeled as a hedonic coalitionformation game between the agents and the tasks thatinteract in order to form disjoint coalitions. Each formedcoalition is mapped to a polling system which consists of anumber of agents continuously collecting packets from anumber of tasks. Within a coalition, the agents can act eitheras collectors that move between the different tasks present inthe coalition for collecting the packet data or relays forimproving the wireless transmission of the data packets. Forforming the coalitions, we introduce an algorithm that allowsthe players (tasks or agents) to join or leave the coalitionsbased on their preferences which capture the trade-offbetween the effective throughput and the delay achievedby the coalition. We study the properties and characteristicsof the proposed model, show that the proposed hedoniccoalition formation algorithm always converges to a Nash-stable partition, and study how the proposed algorithmallows the agents and tasks to take distributed decisions foradapting the network topology to environmental changes,such as the deployment of new tasks, the removal of existingtasks, or the mobility of the tasks. Simulation results showhow the proposed algorithm allows the agents and tasks toself-organize into independent coalitions, while improvingthe performance, in terms of average player (agent or task)payoff, of at least 30.26 percent (for a network of five agentswith up to 25 tasks) relatively to a scheme that allocatesnearby tasks equally among the agents. In a nutshell, bycombining concepts from wireless networks, queuing theoryand novel concepts from coalitional game theory, weproposed a new model for task allocation among autono-mous agents in communication networks which is wellsuited for many practical applications, such as data collec-tion, data transmission, autonomous relaying, operation ofmessage ferry (mobile base stations), surveillance, monitor-ing, or maintenance in next-generation wireless networks.

ACKNOWLEDGMENTS

This work was done during Walid Saad’s stay at theCoordinated Science Laboratory, University of Illinois atUrbana-Champaign, and was supported by the ResearchCouncil of Norway through projects 183311/S10, 176773/S10, and 18778/V11, and in part by a grant from AFOSR. Apreliminary version of this work [39] appeared in theproceedings of the International Conference on GameTheory for Networks (GameNets), May 2009.

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Walid Saad received the BE degree in computerand communications engineering from the Le-banese University, Faculty of Engineering II, in2004, the ME degree in computer and commu-nications engineering from the American Uni-versity of Beirut (AUB) in 2007, and the PhDdegree from the University of Oslo in 2010. FromAugust 2008 to July 2009, he was a visitingscholar in the Coordinated Science Laboratoryat the University of Illinois at Urbana Cham-

paign. From January 2011 to August 2011, he was a postdoctoralresearch associate in the Electrical and Computer Engineering Depart-ment at Princeton University. Currently, he is an assistant professor inthe Electrical and Computer Engineering Department at the University ofMiami, Florida. His research interests include applications of gametheory in wireless networks, coalitional game theory, cognitive radio,autonomous communication, and wireless communication systems(UMTS, WiMAX, LTE, etc.). He was the first author of the papers thatreceived Best Paper awards at the Seventh International Symposium onModeling and Optimization in Mobile, Ad Hoc and Wireless Networks(WiOpt) in June 2009 and at the Fifth International Conference onInternet Monitoring and Protection (ICIMP) in May 2010.


Zhu Han received the BS degree in electronicengineering from Tsinghua University in 1997and the MS and PhD degrees in electricalengineering from the University of Maryland,College Park, in 1999 and 2003, respectively.From 2000 to 2002, he was an R&D engineer ofJDSU, Germantown, Maryland. From 2003 to2006, he was a research associate at theUniversity of Maryland. From 2006 to 2008, hewas an assistant professor at Boise State

University, Idaho. Currently, he is an assistant professor in the Electricaland Computer Engineering Department at the University of Houston,Texas. In June-August 2006, he was a visiting scholar at PrincetonUniversity; in May-August 2007, a visiting professor at StanfordUniversity; and in May-August 2008, a visiting professor at the Universityof Oslo, Norway, and Supelec, Paris, France. In July 2009, he was avisiting professor at the University of Illinois at Urbana-Champion. Hisresearch interests include wireless resource allocation and manage-ment, wireless communications and networking, game theory, wirelessmultimedia, and security. He was a US National Science FoundationCAREER award recipient in 2010. He has been an associate editor ofthe IEEE Transactions on Wireless Communications since 2010. Hewas the MAC Symposium vice chair of the IEEE Wireless Communica-tions and Networking Conference 2008. He was the guest editor for theSpecial Issue on Cooperative Networking Challenges and Applications(IEEE Journal on Selected Areas in Communications), Special Issue onFairness of Radio Resource Management Techniques in WirelessNetworks (EURASIP Journal on Wireless Communications and Net-working), and Special Issue on Game Theory (EURASIP Journal onAdvances in Signal Processing). He is a coauthor of the papers that wonthe Best Paper awards at the IEEE International Conference onCommunications 2009 and the Seventh International Symposium onModeling and Optimization in Mobile, Ad Hoc, and Wireless Networks(WiOpt 2009). He is a senior member of the IEEE.

Tamer Basar received the BSEE degree fromRobert College, Istanbul, and the MS, MPhil,and PhD degrees in engineering and appliedscience from Yale University. After holdingpositions at Harvard University and MarmaraResearch Institute, Gebze, Turkey, he joined theUniversity of Illinois at Urbana-Champaign(UIUC) in 1981, where he currently holds thepositions of Swanlund Endowed Chair, profes-sor of electrical and computer engineering in the

Center for Advanced Study, research professor in the CoordinatedScience Laboratory, and research professor at the Information TrustInstitute. He is also the interim director of the Beckman Institute forAdvanced Science and Technology. He has published extensively insystems, control, communications, and dynamic games, and has currentresearch interests in modeling and control of communication networks;control over heterogeneous networks; resource allocation, manage-ment, and pricing in networks; game-theoretic tools for networks; mobilecomputing; security issues in computer networks; and robust identifica-tion, estimation, and control. He is the editor-in-chief of Automatica andIEEE Expert Now, editor of the Birkhauser Series on Systems & Control,managing editor of the Annals of the International Society of DynamicGames (ISDG), and a member of editorial and advisory boards ofseveral international journals in control, wireless networks, and appliedmathematics. He has received several awards and recognitions over theyears, among which are the Medal of Science of Turkey (1993);Distinguished Member Award (1993), Axelby Outstanding Paper Award(1995), and Bode Lecture Prize (2004) of the IEEE Control SystemsSociety (CSS); Millennium Medal of IEEE (2000); Tau Beta Pi DruckerEminent Faculty Award of UIUC (2004); the Outstanding Service Award(2005) and the Giorgio Quazza Medal (2005) of the InternationalFederation of Automatic Control (IFAC); and the Richard E. BellmanControl Heritage Award (2006) of the American Automatic ControlCouncil. He is a member of the US National Academy of Engineering, amember of the European Academy of Sciences, a fellow of the IEEE andthe IFAC, president-elect of the AACC, a past president of the CSS, andthe founding president of the ISDG.

Merouane Debbah received the MSc and PhDdegrees from Ecole Normale Superieure deCachan, France, in 1999 and 2002, respectively.From 1999 to 2002, he worked for Motorola Labson Wireless Local Area Networks and prospec-tive fourth generation systems. From 2002 to2003, he worked as a senior researcher at theVienna Research Center for Telecommunica-tions (FTW), Austria, working on MIMO wirelesschannel modeling issues. From 2003 to 2007, he

worked as an assistant professor in the Mobile CommunicationsDepartment of the Institut Eurecom (Sophia Antipolis, France). He ispresently a professor at Supelec (Gif-sur-Yvette, France), holder of theAlcatel-Lucent Chair on Flexible Radio. His research interests includeinformation theory, signal processing, and wireless communications. Hewas a recipient of the Best Paper award from the 2007 GeneralSymposium IEEE GLOBECOM as well as Best Student Paper awardsfrom Valuetools 2007 and 2008. He is a WWRF fellow.

Are Hjørungnes received the sivilingeniør(MSc) degree (with honors) from the Departmentof Telecommunications at the Norwegian Insti-tute of Technology in Trondheim in 1995 and thedoktor ingeniør (PhD) degree from the SignalProcessing Group at the Norwegian University ofScience and Technology in 2000. He worked asa professor in the Faculty of Mathematics andNatural Sciences at the University of Oslo,Norway, with office located at UNIK - University

Graduate Center. His main research areas were signal processing,communications, and wireless networks. From August 2000 to Decem-ber 2000, he worked as a researcher in the Tampere International Centerfor Signal Processing at the Tampere University of Technology, Finland.From March 2001 to July 2002, he worked as a postdoctoral fellow in theSignal Processing Laboratory at the Federal University of Rio de Janeiroin Brazil. From September 2002 to August 2003, he worked as apostdoctoral fellow in the Signal Processing Laboratory at the HelsinkiUniversity of Technology in Finland. From September 2003 to August2004, he worked as a postdoctoral fellow at the Digital Signal Processingand Image Analysis Group in the Department of Informatics at theUniversity of Oslo in Norway. He held visiting appointments at the Imageand Signal Processing Laboratory at the University of California, SantaBarbara, the Signal Processing Laboratory of the Federal University ofRio de Janeiro, the Mobile Communications Department at EurecomInstitute in France, the University of Manitoba in Canada, the Alcatel-Lucent Chair at SUP�ELEC in France, the Department of Electrical andComputer Engineering at the University of Houston, and the Electricaland Computer Engineering Department at the University of California,San Diego. From 2007-2011, he served as an editor of the IEEETransactions on Wireless Communications. In June 2010, he was aguest editor of the IEEE Journal of Selected Topics in Signal Processingspecial issue on “Model Order Selection in Signal Processing Systems.”He coauthored the papers that won the Best Paper awards at the IEEEInternational Conference on Wireless Communications, Networking andMobile Computing (WiCOM 2007), the Seventh International Symposiumon Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks(WiOpt 2009), and the Fifth International Conference on InternetMonitoring and Protection (ICIMP 2010). He was a senior member ofthe IEEE. Sadly, he passed away in May 2011.

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IEEE TRANSACTIONS ON MOBILE COMPUTING, …people.cs.vt.edu/~irchen/6204/pdf/Saad-TMC11.pdf · Index Terms—Multiagent wireless networks, game theory, hedonic coalitions, task allocation,