Computer Networks 54 (2010) Contents lists available at ScienceDirect. Computer Networks. journal homepage:

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1 Computer Networks 54 (2010) Contents lsts avalable at ScenceDrect Computer Networks journal homepage: A survey on game theory applcatons n wreless networks Dmtrs E. Charlas, Athanasos D. Panagopoulos * Natonal Techncal Unversty of Athens, School of Electrcal & Computer Engneerng, Moble Rado Communcatons Laboratory, Iroon Polytechnou 9, Zografou, Athens, Greece artcle nfo abstract Artcle hstory: Receved 22 June 2010 Accepted 30 June 2010 Avalable onlne 17 July 2010 Responsble Edtor: I.F. Akyldz Keywords: Wreless Networks Game theory Payoff Coalton Nash equlbrum Resource allocaton Power control Call admsson control Routng Cooperaton ncentves Whle the Qualty of Servce (QoS) offered to users may be enhanced through nnovatve protocols and new technologes, future trends should take nto account the effcency of resource allocaton and network/termnal cooperaton as well. Game theory technques have wdely been appled to varous engneerng desgn problems n whch the acton of one component has mpact on (and perhaps conflcts wth) that of any other component. Therefore, game formulatons are used, and a stable soluton for the players s obtaned through the concept of equlbrum. Ths survey collects applcatons of game theory n wreless networkng and presents them n a layered perspectve, emphaszng on whch felds game theory could be effectvely appled. To ths end, several games are modeled and ther key features are exposed. Ó 2010 Elsever B.V. All rghts reserved. 1. Introducton Game theory s a dscplne amng to model stuatons n whch decson makers have to make specfc actons that have mutual possbly conflctng consequences [1]. It has been used prmarly n economcs, n order to model competton between companes. In the context of wreless networks, game theory may be used as a tool for formng cooperaton schemes among enttes such as nodes, termnals or network provders. Durng the last years, game theory has also been appled to networkng, n most cases to solve routng and resource allocaton problems n a compettve envronment. Recently, ts applcaton was ntroduced n wreless communcatons: the decson makers n the game are ratonal users or networks operators who control ther communcaton devces. * Correspondng author. Tel.: ; fax: E-mal addresses: dcharlas@moble.ntua.gr (D.E. Charlas), thpanag@ ece.ntua.gr (A.D. Panagopoulos). These devces have to cope wth a lmted transmsson resource (.e., the rado spectrum) that mposes a conflct of nterests [2]. In ths artcle we descrbe how game-theoretc frameworks can be set up to address several ssues n wreless networks and survey recent advances n ths area, hghlghtng applcablty to problems such as power control, spectrum allocaton call admsson control, medum access control and routng, among others. Emphass s placed on whch type of game s most approprate for each case, as well as on whch element should be consdered n the development of utlty functons; to ths end several examples of such functons are exposed. 2. Game theory bascs 2.1. Basc concepts Ths secton demonstrates the fundamentals of game theory. For further detals the reader s prompted at [1,3,4]. Game theory s related to the actons of decson /$ - see front matter Ó 2010 Elsever B.V. All rghts reserved. do: /j.comnet

2 3422 D.E. Charlas, A.D. Panagopoulos / Computer Networks 54 (2010) makers who are conscous that ther actons affect each other. A game conssts of a prncpal and a fnte set of players N = {1,2,...,N}, each of whch selects a strategy s 2 S wth the objectve of maxmzng hs utlty u. The utlty functon u (s): S? R represents each player s senstvty to everyone s actons. Accordng to the above, a game can be modeled as G =(P,A,S, p j ) where: P = {1,...,n} denotes the set of players A = {1,...,n} denotes the avalable resources n the game (acton set) S denotes the set of strateges for player,.e. all possble choces from set A p j denotes the payoff assgned to player after choosng resource j. Table 1 presents a mappng between the basc components of a game and the enttes of wreless networks. Two types of games are dstngushed: n non-cooperatve games, each player selects strateges wthout coordnaton wth others. The strategy profle s s the vector contanng the strateges of all players: s = (s ), 2 N = (s 1,s 2,..., s N ). On the other hand, n a cooperatve game, the players cooperatvely try to come to an agreement, and the players have a choce to bargan wth each other so that they can gan maxmum beneft, whch s hgher than what they could have obtaned by playng the game wthout cooperaton [5]. Let N = {1,2,...,N} be a set of n players. Non-empty subsets of N, S,T # N are called a coalton. The coalton form of an n-player game s gven by the par (N,u), where u s the characterstc functon [6]. A coalton that ncludes all of the players s called a grand coalton. The characterstc functon assgns each coalton S ts maxmum gan, the expected total ncome of the coalton denoted u(s). The core s the set of all feasble outcomes that no player or coalton can mprove upon by actng for themselves. The objectve s to allocate the resources so that the total utlty of the coalton s maxmzed. In wreless networks the formaton of coaltons nvolves the sharng of certan resources; however, as the costs of such resource sharng outwegh the benefts perceved by the nodes, users are less lkely to partcpate, compromsng overall network goals Nash equlbrum The equlbrum strateges are chosen by the players n order to maxmze ther ndvdual payoffs. In game theory, the nash equlbrum s a soluton concept of a game nvolvng two or more players, n whch no player has anythng to gan by changng only hs own strategy unlaterally. If each player has chosen a strategy and no player can beneft by changng hs strategy whle the other players keep thers unchanged, then the current set of strategy choces and the correspondng payoffs consttute a nash equlbrum. Some games can be solved by terated domnance, whch systematcally rules out strategy profles. A pure strategy s s strctly domnated for player f there exsts s 0 2 S such that u (s 0,s )>u (s,s ) " s 2 S.Its customary to denote by s the collectve strateges of all players except player Mxed strateges When a player makes a decson, he can use ether a pure or a mxed strategy. If the actons of the player are determnstc, he s consdered to use a pure strategy. If probablty dstrbutons are defned to descrbe the actons of the player, a mxed strategy s used. We denote a mxed strategy avalable to player as r.we denote by r (s ) the probablty that r assgns to s. Clearly, P s j 2S r ðs Þ¼1. Of course, a pure strategy s s a degenerate case of a mxed strategy r, where r (s ) = 1. The space of player s mxed strateges s R. As before, a mxed strategy profle r =(r 1,r 2,...,r N ) and the Cartesan product of the R forms the mxed strategy space R Repeated games In strategc or statc games, the players make ther decsons smultaneously at the begnnng of the game. On the contrary, the model of an extensve game defnes the possble orders of the events. The players can make decsons durng the game and they can react to other players decsons. Extensve games can be fnte or nfnte. A class of extensve games s repeated games, n whch a game s played numerous tmes and the players can observe the outcome of the prevous game before attendng the next repetton. 3. Game theory n wreless networks: a layered perspectve As stated n the ntroducton of the present artcle, the author s ntenton s to collect a wde spectrum of game theory applcatons n wreless networks. In order to provde a coherent presentaton and pont out the varous felds of applcaton, the latter have been categorzed under correspondng OSI Layers. The adopted layered perspectve Table 1 Mappng of game theory elements to networks. Game component Players Resources Strateges Payoffs Enttes, processes or elements of wreless networks Network nodes, servce provders or customers All knds of resources needed by nodes to communcate successfully (spectrum, power, bandwdth, etc.), ncome A decson regardng a certan acton of the player, dependng on the applcaton feld (forward packet, set power level, accept new call, etc.) Estmated by utlty functons, based on QoS merts (delay, throughput, SNR, etc.)

3 D.E. Charlas, A.D. Panagopoulos / Computer Networks 54 (2010) Table 2 Layered presentaton of game theory applcatons. OSI Layer Applcaton feld Specfc applcaton Physcal Power control Power control for CDMA Power control n OFDMA Networks Spectrum allocaton Spectrum sharng- Spectrum transactons MIMO Systems Power management n MIMO Cooperatve communcatons Decode-and-forward cooperaton Data lnk Medum access control Access to slotted Aloha Random access to the nterference channel Network Routng Routng and forwardng Transport Call admsson control Request dstrbuton among provders Call acceptance based on provder and customer context Load control Termnaton of sessons based on provder and customer context Cell selecton Inter-cell and ntra-cell games ams at demonstratng that game theory may be used to solve problems n all aspects of telecommuncatons, whle allowng for possble combnaton of game-theoretc frameworks to acheve cross-layer optmzaton. In most of these games the concept of prcng s also dscussed, snce prcng consttutes a vtal factor n an utlty functon. As depcted n Table 2, several applcaton felds are examned under each layer, whle nterestng approaches are dscussed for each feld; ths however does not mply under any crcumstances that no other applcaton felds exst. The authors have smply ncluded the ones they consder most ndcatve and most helpful for the readers unfamlar wth the usefulness of game theory. In ths pont the authors would lke to note also that processes such as admsson control or load control cannot be assgned explctly to a sngle layer, snce they often deploy cross-layer optmzaton technques and could thus nvolve elements of multple layers. 4. Physcal layer From a physcal layer perspectve, performance s generally a functon of the estmated sgnal-to-nterferenceand-nose rato (SINR) that players/nodes receve. When the nodes n a network respond to changes n perceved SINR by adaptng ther sgnal, a physcal layer nteractve decson makng process occurs. In ths frame, game theory can be appled to allocaton problems concernng resources such as power or spectrum. A sgnfcant aspect that s taken under consderaton n these formulatons s the nterference avodance Power control In the power control problem, each user s utlty s ncreasng n hs sgnal-to-nterference-and-nose rato (SINR) and decreasng n hs power level [7]. If all other users power levels were fxed, then ncreasng one s power would ncrease one s SINR. However, when a user rases her transmsson power, ths acton ncreases the nterference seen by other users, drvng ther SINRs down, nducng them to ncrease ther own power levels. MacKenze and Wcker n [8] formulate a non-cooperatve power control game for a CDMA system. Suppose that users transmt nformaton at the rate R bts/s n L bt packets over a spread-spectrum bandwdth of W (Hz). Let p j be the power transmtted by user j; assumng that users choose ther power levels from the set of non-negatve real numbers, p j 2 [0,1), the sgnal-to-nterference-and nose rato of user j can be defned as SINR j ¼ c j ¼ W R h j p P j 8 j h p þ r ; 2 ð1þ where h j s the path gan from user j to the base staton and r 2 s the power of the background nose at the recever. It s also assumed that the background nose s addtve whte Gaussan nose (AWGN). The utlty functon of user j has the unt of bts/j and can be expressed by u j ðp j ; c j Þ¼ R p j ð1 2 BERðc j ÞÞ L ; ð2þ where BER(j) s the bt error rate acheved by a gven transmsson scheme. If the user s transmt power s too hgh, then he s squanderng precous battery power whle havng lttle mpact on hs bt error rate. The users wll attempt to make the best possble choces, takng nto account that the other users are dong the same thng. Assumng that the users have complete nformaton about each other and that they are completely ratonal, accordng to game theory, they wll choose an operatng pont whch s a nash equlbrum. MacKenze and Wcker [8] also ntroduce two new types of games: the refereed and the repeated power control games. Guntur and Pagann n [9] form a smlar power control game, whch s then expanded to a multcell case. Furthermore, Zhu Han et al. n [10] add a vrtual referee to the mult-cell power control problem. Interference avodance s also examned n [11] under the scope of game theory. Game theory has found smlar applcatons n Orthogonal Frequency Dvson Multplexng Access (OFDMA) networks as well. In these cases the objectve s to mnmze the overall transmtted power under rate and power constrants, by adjustng the rate allocaton over dfferent sub-channels for dfferent users. The authors of [12] model ths problem as a non-cooperatve game between users, consderng t as a water-fllng problem. The soluton of the game provdes the optmal values for both power and

4 3424 D.E. Charlas, A.D. Panagopoulos / Computer Networks 54 (2010) rate that offer the best utlty for a user gven the other users resource allocaton. A game-theoretc approach to allocate power n mult-cell OFDM networks through non-cooperatve games s also presented n [13] Spectrum allocaton The spectrum sharng problem addresses the ssue of how to allocate the lmted avalable spectrum among multple wreless devces. The allocaton of spectrum should utlze as much of the resource as possble; however, when utlzaton s maxmzed, farness can be compromsed. A cooperatve game for dstrbuted spectrum sharng s dscussed n [14]. Accordng to ths approach, the avalable bandwdth s dvded equally nto multple channels. Each node can transmt n any combnaton of channels at any tme and can set ts transmt power on each channel. Recever nodes do not transmt and thus are not consdered as players n the game. Let v = {1,...,K} be the set of avalable channels, B be the aggregate bandwdth, wth each channel havng bandwdth B/K, and N be the number of transmtter nodes n the network. The spectrum sharng game s formulated n [15] as follows: M ¼f1;...;Ng;P x ¼fðp k Þk 2 xjpk P 0; P k2x pk < P max g and P x ¼ P x 1 X...XPx N. Let p 2 Pv and u (p)=c (p), where C (p) s the Shannon capacty:! C ðpþ ¼ B K XK k¼1 log 2 1 þ r 2 K H k pk P 8j Hk j pk j ; ð3þ where p k s the power transmtted by node on channel k, P max s the maxmum transmt power, H k j s the channel gan from j to the recever of on channel k, and r 2 s the thermal nose for the entre bandwdth B. Thus, the utlty functon of node can be approxmated as the Shannon capacty, gven that nodes that are far enough away from node s recevers such that they cause neglgble nterference, are neglected. Smulatons then show that when nterference s hgh, optmal mxed strateges usually nvolve only a sngle node transmttng at a tme. Nyato and Hossan [16] consder n ther work the problem of spectrum sharng among a prmary user and multple secondary users, formng a model for compettve spectrum sharng among secondary users n cogntve rado networks. The payoff of secondary user s n ths case p ðbþ ¼r k b b x þ y X s3 b j A 5; ð4þ b j eb where b s the allocated spectrum sze, B s the set of all avalable strateges, k s the average transmsson rate, r s the revenue, x, y, and s are non-negatve constants, s P 1. Smlar approaches can be found n [17,18]. A smlar problem to spectrum sharng s that of spectrum transactons. Nyato and Hossan [19] study the problem of spectrum prcng n a cogntve rado network where multple prmary servce provders compete wth each other to offer spectrum access opportuntes to the secondary users. Smlarly, the authors of [20] address the problem of non-cooperatve operators tryng to maxmze ther profts by offerng extra spectral resources to other ones. The revenue and costs for prmary operator are calculated n both cases as follows: RevðÞ ¼c M ; 2 Costðq Þ¼c 2 M BW req W q a ð5þ M where c 1 and c 2 denote weghts for the revenue and cost functons respectvely, BW req denotes the bandwdth requrement for a prmary operator and a s the spectral effcency for prmary operator. M s the number of prmary connectons. Based on the aforementoned model, a game can be formulated where the players are the prmary operators offerng spectrum. Ther strategy may be the prce per unt of spectrum p and fnally the payoff for every operator can be the proft (revenue-costs) after the spectrum transacton. The revenue for every operator can be calculated as: Prof ðpþ ¼q p þ Rev Cost ; ð6þ where p denotes the set of prces offered by all players n the game and p ={p 1,...,p N } s the set of prces. The best response functon of operator, gven a set of prces offered by other prmary operators p s B ðp Þ¼arg max p ðpr of ðp ÞÞ MIMO systems The authors of [21] consder nterference characterzaton and management n wreless ad hoc networks usng Multple Input Multple Output (MIMO) technques. Accordng to ths approach, power allocaton n the th lnk s modeled as non-cooperatve games usng the smple utlty functon u = C c p where c s a scalng factor so that the two terms n the prevous equaton have the same unts, C s the achevable data rate of the lnk and p s the lnk transmt power. Smlarly, n [22] non-cooperatve games are formulated, n whch the players are the lnks and the payoff functons are the rates on each lnk. The soluton to the problem s consdered as the water-fllng soluton, whle the nash equlbrum, accordng to the authors, s consdered as fxed-pont Cooperatve communcatons Chen and Kshore [23] have developed a cooperatve game-theoretc analyss of decode and forward cooperatve communcatons for addtve whte Gaussan nose (AWGN) and Raylegh fadng channels, as two-state Markov models. Accordng to ths model, the termnals, whch consttute the players, communcate over orthogonal channels to a common destnaton node. The authors propose two alternatves for the payoff: t may be consdered equal to the Shannon capacty or to the transmsson relablty, whch s equal to 1 mnus the bt error rate. The games are assumed to be montored by an entty whch ether rewards or punshes nodes (by ncreasng or reducng the transmsson power respectvely) based on ther behavor.

5 D.E. Charlas, A.D. Panagopoulos / Computer Networks 54 (2010) Data lnk layer Game theory applcatons regardng the data lnk layer nvolve the medum access control problem. In these games, selfsh users seek to maxmze ther utlty by obtanng an unfar share of access to the channel. Ths acton, though, decreases the ablty of other users to access the channel Medum access control A fne example of such games s the work of MacKenze and Wcker [3,24], who model random access to slotted Aloha. Accordng to ths case, users wsh to transmt as soon as possble. However, f multple users try to transmt smultaneously, all accesses wll fal. Addtonally, unsuccessful attempts to transmt may cost. In slotted Aloha, tme s dvded nto slots and through a specfc method of synchronzaton. All users know where the slot boundares are located; when a user wshes to access the shared channel he wats untl the next slot boundary and then he starts attemptng to transmt. If two or more users try to transmt n the same slot, the users become backlogged and must try to repeat the transmsson n a future slot. Let G(n) be the game n whch there are currently n users. In each stage of G(n) each of the players must decde whether to transmt (T) or wat (W). If one player decdes to transmt and the rest decde to wat, the player who transmts wll receve a payoff of 1, and each of the other (n 1) players wll play G(n 1) n the next perod. If ether no users transmt or more than one user transmt, all players wll play G(n) agan n the next perod. Players place a lower value on payoffs n later stages than on current payoffs. Ths s represented by a per perod dscount factor d < 1. Let u,n represent user s utlty from playng G(n) and let K be a random varable denotng the number of other users who transmt n a gven slot. The utlty functons for each acton are then [24]: P½K ¼ 0Š u ;n ðtþ ¼ 1 d P½K > 0Š ; d P½K ¼ 1Š u ;n ðwþ ¼ 1 d P½K 1Š u ;n 1: ð7þ Ths game has symmetrc nash equlbrum strateges. Smeone et al. [25] dscuss a game formulaton of a basc two-by-two nterference channel wth random packet arrvals and random access. In ths model, tme s slotted and transmsson of each packet takes one slot. Let us assume that n ths non-cooperatve game transmtter transmts wth probablty p ð1þ f the other transmtter has no packet n queue, and p ð2þ otherwse. The set of all feasble transmsson probabltes s defned as P ðq j Þ¼ h q ¼ p ð1þ under the constrans p ð1þ p ð2þ p ð2þ T ð1þ : 0 6 p ; p ð2þ 6 1 ¼ 0 ) p ð2þ > 0; p ð2þ ¼ 0 ) p ð1þ > 0; ; ð8þ ¼ 0 ) p ð2þ j > 0: ð9þ Assumng that the state (backlog) of the system at the tth slot s descrbed by a varable S (t) that takes values n the set S = {S1,S2,S3,S4} = {(0,0), (1,0), (0,1), (1,1)}, where each tuple descrbes the backlog of the two transmtters (1 means that the transmtter has a packet to transmt, whle 0 mean t does not), the payoff s modeled as R ðpþ¼p qðþ ðpþp ð1þ q ð1þ þ p 4 ðpþ½p ð2þ ð1 p ð2þ j Þq ð1þ þ p ð2þ p ð2þ j q ð2þ ; ð10þ where q (1) = 2, q (2) = 3 and p q() (p)=p [S (t) = S k ], k = 1, 2, 3, 4 are steady state probabltes. 6. Network layer Functonaltes of the network layer nclude the establshment of routes and the forwardng of packets along those routes. In most cases game theory may be appled to ad a node n determnng whch the optmal route s or decdng whether t should forward a receved packet or not. The latter are referred to as forwardng games. Game theory s a valuable asset n ths context due to the fact nodes need to decde ndvdually on ther actons, whle mantanng knowledge on the behavor of others. Snce each node wshes to preserve ts energy n order to be able to send as much traffc as possble, forwardng a packet for another node s not ratonal, at least at frst glance Routng and forwardng The games formulated here are non-cooperatve and take place between a par of nodes, denoted as and -. Varatons such as Mn Max games or Bottleneck games can be also formulated [26]. In the routng problem, the source nodes can be vewed as the players n the game. The acton set avalable to each player s the set of all possble paths from the source to the destnaton. In wreless ad hoc networks for example, nodes communcate wth far off destnatons usng ntermedate nodes as relays. Snce wreless nodes are energy constraned, t may not be n the best nterest of a node to always accept relay requests. On the other hand, f all nodes decde not to expend energy n relayng, then network throughput wll drop dramatcally. For ths reason, ad hoc and peer-to-peer networks sometmes operate as voluntary resource sharng networks, relyng on users wllngness to spend ther own resources for the common good [27]. In[28] the utlty functon of such a game s modeled as U j (s)=a j (s)+b j (s), where a j ðsþ ¼ a j P2N; j s s the beneft accrued by a user from others sharng of ther resources and b j (s)=b j (s j ) s the beneft (or cost) accrued by sharng one s own resources wth others, s beng the jont acton taken by all players (s = 0 stands for sharng and s = 1 for not sharng). The latter may be negatve, snce there may be a cost to partcpatng n the network (such as faster depleton of a node s energy resources) or postve, f fnancal ncentves for partcpaton exst or f the user derves satsfacton n dong so. Concernng forwardng games, a wde varety of utlty functons has been proposed n ths context; the majorty of them consder metrcs such as the node s forwardng rato and energy consumpton. For example, DARWIN [29]

6 3426 D.E. Charlas, A.D. Panagopoulos / Computer Networks 54 (2010) consders the followng payoff, gven that a s the reward a node receves for forwardng a packet and p s the probablty that node drops a packet. u ¼ 1 þ 1 2a 1 p 2a 2a 1 p : 7. Transport layer ð11þ At the transport layer, game-theoretc models have been manly developed to analyze the effectveness of congeston control algorthms. Congeston avodance control refers to controllng the load of the network by restrctng the admsson of new user s sessons and resolvng the unwanted overload stuatons. Admsson control and load control consttute key mechansms regardng Rado Resource Management (RRM) Call admsson control Admsson control takes place each tme a new sesson request s receved and decdes whether t should be allocated resources or be rejected due to lack of resources. Its basc goal n cellular networks s to control the admsson of new sessons wthn the network wth the goal of mantanng the load of the network wthn some boundares. The decson about the target network can be based on ether user or network/operator crtera [30 32]. Fg. 1 depcts two dfferent types of ths knd of game, whch wll be analyzed n ths secton Provder vs. provder In ths knd of games the networks consttute the players. As ndvdual players n the game, the access networks wll try to choose the request that best fts ther characterstcs. Such a game may be played n rounds. In each round of the game the networks must decde whch request wll maxmze ther payoff and then select t. Once a request s selected t s removed from the set of servce requests and the game s repeated, untl all requests have been selected. A typcal example can be found n [33]. The proposed game s non-zero-sum and non-cooperatve, snce a player s unable to bnd and enforce agreements wth other players Customer vs. provder The man goal of such schemes s to maxmze not only the QoS offered to customers, but also the provder s gan, therefore balancng the nterests of both partes. Such an attempt has been modeled n [34 36]. The authors there consder that each customer has a contract wth a specfc servce provder, thus hm beng the default network choce ( home provder); nevertheless, f case of nsuffcent resources, the customer s free to pursue hgher QoS at another provder, gven that there s some knd of federaton agreement between the vsted and the home provder as n roamng (possbly under a small monetary penalty). Suppose that there are N users and M servce provders, whch means that each user at any tme can choose any provder, gvng a total of M N possble states. Each user-provder combnaton s consdered as a two-player game G j,16 j 6 M. The proposed game s non-cooperatve because, on the one hand, the servce provders wsh to maxmze ther revenue and, on the other hand, the users wsh to maxmze the qualty of servce receved, keepng at the same tme the expenses as low as possble. Snce these two goals are obvously contradctory, the players do not have the slghtest motvaton to cooperate. The game s also nonzero-sum, snce an ncrease n one player s payoff does not mply a decrease n the other player s payoff. The user s revenue expresses n monetary value the qualty of servce offered to hm, takng nto account the cost, and may be modeled as R = Uq C, whereu expresses the customer s utlty functon, q s a constant factor mappng the utlty value to monetary value and C s the cost of the servce from the customer s pont of vew [34 36]. It s also assumed that the provder s bllng scheme takes nto account the QoS percentage offered to customers, meanng that the customer pays an amount proportonal to the level of QoS he receves. In bblography, n most cases, user satsfacton s montored through utlty. For nstance, n [12], utlty s approxmated by a sgmod functon as U ¼ 1 1þe aðb PbÞ where Fg. 1. Call admsson control games.

7 D.E. Charlas, A.D. Panagopoulos / Computer Networks 54 (2010) P b s the packet blockng probablty and a, b are constants whch determne the steepness and the center of the curve. Exact user utlty functons can be obtaned through feld tests and user surveys. As far as the soluton of the game s concerned, two cases are dstngushed. Assumng the case where the system s not full, the user request wll be accepted and the probablty that a customer leaves s near to zero. In ths case there s a nash equlbrum, when the servce provder accepts the request whle the user remans wth the provder. Assumng now the case where the system s loaded to a certan extent or even overloaded, the user request may be not accepted and the probablty that a customer leaves s non zero. Even n ths case, there s also a pure strategy nash equlbrum whch depends on the relaton between some terms n the payoffs. The new request s accepted f the revenue generated from admttng the request s greater than the possble revenue loss s the user leaves. Otherwse, the provder s better to reject the request Load control The scheme descrbed prevously for admsson control has also been expanded for load control n [36]. The man dfference s that ths game s played perodcally whle the sessons are runnng. Through ths process t s possble to termnate sessons that greedly consume the system s resources, causng ths way degradaton to the QoS offered to the rest of the customers and thus reducng the provder s total revenue. Moreover, unsatsfed customers are granted the opportunty to seek more effcent networks, based on ther preferences. Accordng to ths scheme, f the QoS of at least one servce type s found below the acceptance threshold, then the global load control game s trggered, durng whch games are played between the provder and all runnng sessons. Ths game may result n ether dsapponted customers leavng the provder or the provder termnatng unproftable customers. If ether one decdes that a connecton should be termnated, then the sesson ends and the customer s prompted to another servce provder. Penalty s submtted only f the customer chooses to leave wllngly. On the other hand, f the global game s not trggered and at least one sesson presents a QoS below the acceptance threshold, then the local load control game s trggered. In ths case, a game s played between the provder and each sesson that trggered the game, leavng the other sessons unaffected. Ths type of game may also result n some sessons beng termnated Cell selecton Cell selecton s responsble for guaranteeng the requred QoS by always keepng the moble camped on a moble staton wth good enough qualty. The goal of cell selecton procedures s to determne whch base staton s the optmal choce. Gao et al. [37] formulate the cell selecton problem as the two-ter game. In the frst ter,.e., n nter-cell game, the moble statons select the cell accordng to the optmal cell selecton strategy derved from the expected payoff. In the second ter,.e., n ntracell game, the moble statons choose the proper tme frequency resource n the servng cell to acheve the hghest payoff. 8. Dscusson In ths secton the authors dscuss certan ssues that are relevant wth the applcaton of game theory n wreless network. Table 3 summarzes the key elements of the games descrbed throughout the prevous sectons Challenges n the use of game theory The use of game theory n wreless networks unfortunately comes wth a set of challenges, the most mportant of whch are the followng ones: Assumpton of ratonalty Game theory s founded on the hypothess that each player plays ratonally and thus seeks hs best nterest n a ratonal manner. When dealng wth nodes or termnals however ths behavor cannot be always guaranteed. Assumpton of wllngness to cooperate In cooperatve games t s assumed that players wll collaborate n order to maxmze ther profts. A sgnfcant problem s that players sometmes choose to behave selfshly or even cheat n order to optmze ther own proft. For ths reason, n certan occasons, ncentve mechansms for cooperaton, as well as dsncentves aganst cheatng need to be formulated. Choce of utlty functons/ payoff calculaton Ths s unquestonably the most challengng part of a game-theoretc framework, snce the utlty functon nterprets the player s percepton of performance and satsfacton. Utlty functons also show the trade-offs the player s wllng to make, usually between acqurng more resources and savng money. Not guaranteed exstence of equlbrum In game-theoretc formulatons an analyss s often requred to check f they reach a nash equlbrum. Even f an equlbrum s reached however, the exstence of multple equlbra s not always excluded. In such case the most effcent and stable one has to be sought Cooperaton ncentves In several cases, optmzaton ssues requre collaboraton among nodes. Nevertheless, cooperaton cannot be taken for granted; even though n most cases players do obtan the optmal result by sharng resources wth others, n certan cases t s not clear enough for them why they should not act selfshly or even not try to cheat. Nodes exhbtng such behavor are termed selfsh and malcous correspondngly. The basc dea for node punshment s that nodes should be rewarded or penalzed based on ther behavor. Nodes that offer resources should be aded. On the other hand, selfsh nodes should be gradually solated from the network.

8 3428 D.E. Charlas, A.D. Panagopoulos / Computer Networks 54 (2010) Table 3 Collectve nformaton on game theory applcatons. Specfc applcaton Objectve Game type Players Power control for CDMA Set transmsson power n order to maxmze SNIR Non-cooperatve Users/termnals wth mnmum nterference. Power control n OFDMA networks Mnmze the overall transmtted power under rate Non-cooperatve Users/termnals and power constrants. Spectrum sharng spectrum transactons Dstrbute spectrum to maxmze utlzaton and farness. Cooperatve/ noncooperatve Users/termnals, servce provders Power management n MIMO Power allocaton n lnks to mnmze nterference. Non-cooperatve Lnks Decode-and-forward cooperaton Power allocaton problem Cooperatve/ noncooperatve Users/termnals Access to slotted Aloha Model random access to slotted Aloha to mnmze Non-cooperatve Users/termnals collsons. Random access to the nterference Share access to an nterference channel Non-cooperatve Users/termnals channel Routng and Forwardng Decde f a packet from another node should be Non-cooperatve Users/termnals forwarded or not. Choose the optmal path. Request dstrbuton among provders Dstrbute servce requests among a set of provders Non-cooperatve Servce Provders n an optmal way. Call acceptance based on provder and customer context Decde f acceptance of a servce request would be benefcal to both players Selecton of the optmal Non-cooperatve Servce provder User/ termnal Servce Provder. Termnaton of sessons based on provder and customer context Decde f termnaton of an ongong sesson would be benefcal to ether player. Non-cooperatve Servce provder User/ termnal Inter-cell and ntra-cell games Decde whch cell can best fulfll servce requrements. Non-cooperatve Servce provder User/ termnal, servce provders In wreless networks, ncentve mechansms may be appled to urge players to cooperate nstead of pursung ther own nterest. Reputaton and prcng are the man concepts around whch cooperaton ncentve mechansms are bult, provdng respectvely reputaton-based and credt-based mechansms. Credt-based systems have been used wdely n routng formulatons. The basc dea of these systems s to use notonal credt, monetary or otherwse, to pay off users for forwardng packets comng from other users. Ths acts as a compensaton for transmsson and battery costs. These credts can then be used to forward ther own packets through other users, resultng n an ncentve to act as relay ponts. Users who do not cooperate wll not be able to use the network themselves, havng not earned any credts. One of the most well known credt-based schemes called Sprte [38] uses the dea of credt to solve the problem of routng n ad hoc networks of self-nterested nodes. The basc advantage of credt based systems s that they succeed n a large scale to stmulate cooperaton n networks wth selfsh nodes. Moreover, credts are useful when an acton and ts reward are not smultaneous. On the other hand, reputaton management systems can be categorzed n centralzed and decentralzed and the reputaton s estmated ether n a central hub staton or at each node ndvdually. In the context of wreless networks, reputaton reflects the player s wllngness to contrbute to the whole network by sharng resources, for nstance to forward packets or not. The most accepted game theoretc framework that s used to analyze reputaton s that of repeated games. Reputaton systems may fnd applcaton n self-organzed networks, such as 4G, where there are varous heterogeneous components. One of the man advantages of ths knd of ncentves s that t reles on observatons from multples sources, nstead on the judgment of a sngle entty; t s therefore a rather subjectve means of evaluaton, relatvely resstant to the dffuson of false nformaton from a small number of lyng nodes. CONFIDANT [39] s a protocol whch detects and solates msbehavng nodes. In ths approach nodes have a montor for observatons, reputaton records for frsthand and trusted second-hand observatons, trust records to control trust gven to receved warnngs, and a path manager for nodes to adapt ther behavor accordng to reputaton. On the other hand, n OCEAN [40] only frsthand observatons are consdered Game theory and 4G Cooperaton s the major ssue n such self-organzed communcaton systems, because users/nodes are concerned mostly for ther own profts. They usually show selfsh behavor whch s catastrophc for the connectvty and the whole throughput of the wreless mesh network. The success of 4G wll consst n the combnaton of network and termnal heterogenety, as stated n [15,41,42]. Network heterogenety guarantees ubqutous connecton and provson of common servces to the user, ensurng at least the same level of QoS when passng from one network s support to another one. Moreover, due to the smultaneous avalablty of dfferent networks, heterogeneous servces wll also be provded to the user [43,44]. The concept of node cooperaton ntroduces a new form of dversty that results n an ncreased relablty of the communcaton, leadng both to the extenson of the coverage and the mnmzaton of the power consumpton. In fact, moble termnals are less susceptble to the channel varatons and shadowng effects and can transmt at lower power levels n order to acheve a certan throughput, thus ncreasng ther battery lfe. Furthermore, cooperatve

9 D.E. Charlas, A.D. Panagopoulos / Computer Networks 54 (2010) transmsson strateges may ncrease the end-to-end capacty and hence the spectral effcency of the system [45]. Throughout the modeled games and applcatons hghlghted so far, s should be clear how game-theoretc solutons may effectvely predct/smulate realstc user behavor n compettve or cooperatve scenaros. Snce n 4G the most effcent allocaton of resources s requred, user cooperaton may be modeled accordng to the prncples of game theory. The authors envson a novel future archtecture where users may form freely and dynamcally resource sharng groups, where users are expected to share as many resources they see best for ther own nterests. Game-theoretc backgrounds can easly fabrcate mechansms for rewardng generous users or punshng selfsh ones. Another possble applcaton of game theory n 4G nvolves the resource or even clent exchange among dfferent networks or even provders, as dscussed n prevous Sectons. 9. Concludng remarks In ths survey the authors have attempted to demonstrate how game theory can be appled to wreless networkng. Followng a layered perspectve, t has been explaned how to capture wreless networkng problems n game-theoretc formulatons, emphaszng on whch game type best suts each applcaton feld and on how the correspondng utlty functon may be constructed. The purpose of ths survey was to gude the nterested readers famlar wth computer scence through the bascs of both non-cooperatve and cooperatve game theory and to help them ntegrate ths fascnatng tool nto ther own studes. References [1] D. Fudenberg, J. Trole, Game Theory, MIT Press, [2] D. Nyato, E. Hossan, Rado resource management games n wreless networks: an approach to bandwdth allocaton and admsson control for pollng servce n IEEE , Wreless Communcatons, IEEE 14 (1) (2007) [3] Allen B. MacKenze, Luz A. 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10 3430 D.E. Charlas, A.D. Panagopoulos / Computer Networks 54 (2010) [35] P. Vlacheas, D. Charlas, E. Tragos, O. Markak, Maxmzng qualty of servce for customers and revenue for servce provders through a noncooperatve admsson control game, n: ICT Moble Summt 2008, Stockholm, June [36] Dmtrs E. Charlas, Athanasos D. Panagopoulos, Panagots Vlacheas, Ourana I. Markak, Phlp Constantnou, Congeston avodance control through non-cooperatve games between customers and servce provders, n: Frst Internatonal Conference on Moble Lghtweght Wreless Systems (Moblght 2009), Athens, Greece, May [37] Ln Gao, Youyun Xu, Xnbng Wang, Athanasos V. Vaslakos, A game approach for cell selecton and resource allocaton n heterogeneous wreless networks, IEEE/ACM Transactons on Networkng, n press. [38] S. Zhong, J. Chen, Y.R. Yang, Sprte: A smple, cheat-proof, credtbased system for moble ad-hoc networks, n: INFOCOM, [39] S. Buchegger, J.-Y.L. Boudec, Performance analyss of the Confdant protocol: cooperaton of nodes farness n dynamc ad-hoc networks, n: IEEE/ACM Workshop on Moble Ad Hoc Networkng and Computng (MobHOC), June [40] Sorav Bansal, Mary Baker, Observaton-Based Cooperaton Enforcement n Ad hoc Networks, Stanford Techncal Report, [41] S. Frattas, H. Fath, F.H.P. Ftzek, M. Katz, R. Prasad, Defnng 4G technology from the user perspectve 2006, n: IEEE Network Magazne, 20(1), pp [42] M. Katz, F.H.P. Ftzek, Cooperatve technques and prncples enablng future 4G wreless networks, n: The Internatonal Conference on EUROCON, [43] We Shen, Qng-An Zeng, Resource allocaton schemes n ntegrated heterogeneous wreless and moble networks, ACM Journal of Networks 2 (5) (2007). [44] Q. Zhang, F.H.P. Ftzek, Marcos Katz., Evoluton of heterogeneous wreless networks: cooperatve networks, n: Thrd Internatonal Conference of the Center for Informaton and Communcaton Technologes (CICT) Moble and wreless content, servces and networks - Short-term and long-term development trends, Copenhagen, Denmark, November [45] S. Frattas, B. Can, F. Ftzek, R. Prasad, Cooperatve servces for 4G, n: 14th IST Moble & Wreless Communcatons, Dmtrs E. Charlas s a Ph.D. canddate n the Department of Electrcal Engneerng of the Natonal Techncal Unversty of Athens (NTUA). He receved hs MBA n Techno-Economc Systems n 2008 and hs Dploma n Electrcal Engneerng from NTUA n He has worked as a Research Assstant n the Telecommuncatons Laboratory of the Insttute of Communcaton and Computer Systems (ICCS-NTUA). He s currently wth the Moble Radocommuncatons Laboratory of ICCS-NTUA. Hs research nterests nclude moble servces, qualty of servce, wreless communcatons, resource allocaton and game theory applcatons. Dr. Athanasos D. Panagopoulos receved the Dploma Degree n Electrcal and Computer Engneerng and the Dr. Engneerng Degree from Natonal Techncal Unversty of Athens (NTUA) n July 1997 and n Aprl 2002 respectvely. Snce May 2008, he s Lecturer n the School of Electrcal and Computer Engneerng of NTUA. He has publshed more than 70 papers n peer revewed nternatonal journals and transactons and more than 80 papers n conference proceedngs. He has been nvolved n numerous R&D projects funded by European Unon. Hs research nterests nclude moble computng technologes, rado communcaton systems desgn, wreless and satellte communcatons networks and the propagaton effects on upper layer communcaton protocols. He s a Senor Member of IEEE.