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A Game Theory-based Approach to Reducing

Interference in Dense Deployments of Home

Wireless Networks

Josephina Antoniou

and Andreas Pitsillides

Department of Computer Science

University of Cyprus

P.O. Box 20537, CY-1678

Nicosia, CYPRUS

{antoniou.iosifina,

andreas.pitsillides}@ucy.ac.cy

Lavy Libman

School of Information Technologies

University of Sydney

Sydney, NSW 2006

Australia

lavy.libman@sydney.edu.au

Abstract—Urban residential areas are becoming increasingly

dense with more and more home networks being deployed in

close proximity. The paper considers a dense urban residential

area where each house/unit has its own wireless access point (AP),

deployed without any coordination with other such units. In this

situation, it would be much better if neighbouring APs — i.e.,

APs that are physically close to each other — would form groups,

where one member of the group would serve the terminals of

all group members in addition to its own terminals, while the

other access points of the group can be silent or even turned

off, thus reducing interference and increasing overall Quality of

Experience (QoE). The fact that participating units are deployed

without any coordination makes the overall QoE vulnerable

to the selfish behaviour of each unit. We propose a protocol

where each unit operates in an equilibrium of a cooperative-

neighbourhood game. We show using a game theoretic model

that there exists a motivation for APs to enter and remain in

cooperative neighbourhoods, in which interference is decreased

due to the voluntary cooperation of the neighbours.

I. INTRODUCTION

The paper considers a dense urban residential area where

each house/unit has its own wireless access point (AP),

deployed without any coordination with other such units.

Lacking any control regarding the efficient utilization of the

communication channel, it is quite common for a terminal

served by one of the APs to be within the signal range of

multiple alternative APs. Since all APs are in competition

for the same communication resource (radio channel), and

the current standards dictate that at any given time every

terminal must be rigidly associated with one particular AP, this

situation results in increased interference and consequently a

low utilization efficiency of the radio resource.

In a dense deployment, it would be much better for indi-

vidual APs that are in physical proximity to each other to

form groups, where one member of the group would serve

the terminals of all group members in addition to its own

terminals, so that the other access points of the group can

be silent or even turned off, thereby reducing interference

and increasing overall Quality of Experience (QoE). These

groups would include only members whose signal strength

is sufficient to serve all group members, so that the access

point that would be responsible of serving the terminals of a

particular group or neighbourhood could change on a rotating

basis, to allow all group members to equally serve and be

served. Since there is no centralized entity that can control the

APs and force them to form cooperative groups, the creation of

such groups must be able to arise from a distributed process

where each AP makes its own decisions independently and

rationally for the benefit of itself and its terminals. Game

theory is an appropriate tool to model such decentralized

schemes.

In this paper, we model the idea of cooperative neigh-

bourhhoods as a game and show that a group cooperative

strategy in equilibrium, i.e. a strategy for units to voluntarily

participate in a group where members serve terminals on a

rotating basis, has the property that a unit participating in

the group strategy is more likely to gain more in terms of

QoE, than a unit defecting from such cooperation. In fact,

to maintain robustness against uncoordinated deployments in

dense residential areas, we propose a protocol with point

of operation the game theoretic equilibria of a game, which

we will henceforth refer to as the cooperative-neighbourhood

game.

We further propose a protocol for the participating units

to operate in the associated equilibrium point of the game

to achieve the reduced interference. Numerical results for the

cooperative-neighbourhood game provide evidence both to the

robustness of the proposed protocol, as well as to the improved

overall QoE.

The paper is organized as folows. Section II gives an

overview of related work; specifically, section II-A discusses

wireless deployment in urban environments whereas sec-

tion II-B describes the use of game theoretic approaches

in distributed situations, and introduces the idea of a group

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strategy, which is also used in the work presented in this paper.

Section III describes the studied situation in game theoretic

terms and particularly parallelizes it to a repeated prisoner’s

dilemma, proposing a group strategy in a given neighbourhood

that aims to motivate cooperation (section III-A) through

the payoffs received by each unit individually. Section III-B

provides a numerical comparison of the proposed cooperative

strategy with a defecting strategy. Finally, Section IV describes

a protocol that is based on the equilibrium point of the

cooperative neighbourhood game and section V offers some

conclusions and future work directions.

II. RELATED WORK

A. Wireless deployments in urban environments

The density of wireless networks in urban residential areas

is on the rise with more and more home networks being

deployed in quite close proximity, enabled by the low cost

and easy deployment of off-the-shelf 802.11 hardware and

other personal wireless technologies. It is not uncommon for

a wireless station to be within range of dozens of access

points [1], while the IEEE 802.11 standard only offers 3 non-

overlapping channels. In this sense, urban areas are becoming

similar to campus-like environments; however, in organiza-

tions and campuses experts can carefully control and manage

interference of access points by planning the setup of the

network in advance [2]. On the other hand, wireless networks

in urban residential environments have the following two

characteristics that make their deployment more challenging:

1) The network is unplanned, thus aspects of planning such

as coverage and interference cannot be controlled. De-

ployments are mostly spontaneous, resulting in uneven

density of deployment.

2) The network is unmanaged, lacking aspects such as

efficient placement of access points, troubleshooting and

adapting to network changes such as traffic load, as well

as security issues.

The authors of [1] use the term chaotic deployments or

chaotic networks to refer to such a collection of wireless

networks which are unplanned and unmanaged. However, they

do mention advantages of such chaotic networks, for instance

easily enabling new techniques to determine location [3] or

providing near ubiquitous wireless connectivity [4]. The main

disadvantage of these chaotic deployments is that interference

can significantly affect end-user performance, while being hard

to detect [5]. In this paper we consider a solution based

on “virtualization” among the interfering APs, where APs

serve each others’ clients on a rotating basis. The security

implications of allowing association of clients across APs from

multiple owners have been addressed and resolved in [6]. In

this paper we focus on the incentive aspect, and propose a

framework to ensure that the APs are indeed motivated to

provide service to each others’ clients.

B. Strategical decision-making

We consider in this paper the interactions between the

individual homes/units in dense urban deployments of wire-

less networks. Describing and analysing interactions between

independent, selfish entities is a situation that makes a good

candidate to be modeled using the theoretical framework of

Game Theory. Game Theory provides appropriate models and

tools to handle multiple, interacting entities attempting to make

a decision, and seeking a solution state that maximizes each

entity’s utility, i.e. each entity’s quantified satisfaction. Game

Theory has been extensively used in networking research as

a theoretical decision-making framework, e.g. for routing [7],

[8], congestion control [9], [10], resource sharing [11], [12],

and heterogeneous networks [13], [14].

In this paperwe concentrate

Dilemma/Iterated Prisoner’s Dilemma game model. The

Prisoner’s Dilemma and Iterated Prisoner’s Dilemma [15]

have been a rich source of research scrutiny since the 1950s.

However, the publication of Axelrod’s book in 1984 [16]

was the main driver that boosted the concept to the attention

of other areas outside of game theory, as a model for

promoting cooperation. The empirical results of the Iterated

Prisoner’s Dilemma (IPD) tournaments organized by Axelrod

have influenced the game theory, machine learning and

evolutionary computation communities. It has been shown

that adaptive players, learning from the games in which they

are involved, are more likely to survive than non-adaptive

players in evolutionary IPD [17].

Group strategies have become popular in the 2004 and

2005 IPD tournaments [18], because they performed ex-

tremely well and defeated well-known strategies in round-

robin competitions. These mechanisms identified an opponent

according to its response to a certain sequence of cooperate

and defect actions. In particular, the authors in [19] show that

the members of such a group strategy are able to use a pre-

arranged sequence of moves that they make at the start of

each interaction in order to recognise one another, and that

by coordinating their actions they can increase the chances

that one of the team members wins the round-robin style

tournament.

Particularly, in the 2004 tournament, a team from the

University of Southampton introduced a group of strategies,

which were designed to recognize each other through a known

series of five to ten moves at the start of each game. Once two

Southampton players recognized each other, they would act as

a ‘master’ or a ‘slave’. A master will always defect while a

slave will always cooperate in order for the master to win the

maximum payoff. If a Southampton player recognized that

the opponent was not a partner, it would immediately defect

to minimise the score of the opponents. The Southampton

group strategy is modified and used in this paper to motivate

cooperation between group members in a neighbourhood of a

dense urban wireless deployment.

onthePrisoner’s

III. COOPERATIVE NEIGHBOURHOODS

Currently, dense residential deployments of home wireless

networks consist of uncoordinated APs that serve their ter-

minals individually. The APs do not form groups and share

the communication channel, which is an unmanaged common

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resource, resulting in a low utilization efficiency due to the

competition between the APs and the interference it causes.

This interference can be reduced if the APs can form groups

according to their location, such that any APs belonging

to the same group can serve any terminal associated with

any of the other group members. It is possible for an AP

to recognize its neighbourhood from the signals it receives,

having a knowledge of the required signal strength thresholds

that would serve its terminals in a satisfying manner. In such a

neighbourhood only one of the APs needs to assume the role

of a leader, while the others can remain silent, and thereby

minimize the interference and improve the overall quality of

experience for all terminals involved. The role of the leader

can be assumed on a rotating basis. Of course, in order to

take part in a cooperative neighbourhood, the APs need to

be motivated to act cooperatively, i.e. have an incentive to be

silent or turned off while it is the turn of another AP to serve,

and to serve everyone’s terminals once their own turn comes.

We show how such a distributed protocol can be sustained in

the equilibrium point of a game model where each AP can

make an independent decision whether or not to participate in

such a neighbourhood.

The interactions in a cooperative neighbourhood can be

modelled as a game between the participating units, where

each member of the group has two choices at any given time:

(a) to cooperate with its group members or (b) to defect from

cooperation.1Which of the two behaviours to select in each

round depends on the strategy of behaviour that a player has

decided to follow during the repeated game. The strategy of

each player, i.e. each unit, is selected such that it results in the

highest possible payoff for the particular player. We refer to

such interaction between any two neighbours as a cooperative-

neighbourhood game.

Consider a game between 2 neighbouring units, interacting

as follows.

Definition 1 (Cooperative-Neighbourhood game): Let each

unit have a choice between two actions, cooperate or defect,

when interacting with a neighbouring unit. Let cooperation

have one of two outcomes: α = f(x?), when the interacting

unit also cooperates, and α?= f(x), when the interacting

unit defects, where x represents the level of interference, x >

x?, and α represents a quantification of QoE, α > α?. Let

defection have one of two outcomes: β = f(x?), when the

interacting unit also cooperates, and β?= f(x), when the

interacting unit defects, where β, much like α represents a

quantification of QoE, β > β?, and the relationship between

α and β is expresed as follows: α?≤ β?< α < β. Given that

both interacting units choose their actions, they both aim to

maximize their payoffs.

We draw a parallel between the cooperative-neighbourhood

game and a Prisoner’s Dilemma type of game. The classical

Prisoner’s Dilemma decision is whether at any point in time

1Note that units may be a part of more than one neighbourhood, i.e.

receive a good signal from peers that are in different neighbourhoods. In

the basic case, for simplicity, we consider that each unit is part of only one

neighbourhood.

to cooperate with an opponent or defect from cooperation.

Both players make a decision without knowing the decision

of their opponent, and only after the individual decisions are

made, these are revealed. Mutual cooperation has a reward for

both players, specifically the second highest payoff that can

be achieved by a player. However, such decision entails the

risk that in case the other player defects, then the cooperative

player will receive the least possible payoff. Given the risk

of cooperation, it is very tempting to defect because if the

opponent cooperates, then defecting will result in the highest

possible payoff, although, if the other opponent also defects

then the payoff received by both players will only be slightly

better than the worst possible payoff. Definition 2 describes a

Prisoner’s Dilemma kind of game.

Definition 2 (Prisoner’s Dilemma type of game):

Consider an one-shot strategic game with two players in

which each player has two possible actions: to cooperate with

his opponent or to defect from cooperation. Furthermore,

assume that the two following additional restrictions on the

payoffs are satisfied:

1) The order of the payoffs is shown in Table I for each

player j ∈ {1,2} and is such that Aj> Bj> Cj> Dj.

2) The reward for mutual cooperation should be such that

each player is not motivated to exploit his opponent or be

exploited with the same probability, i.e. for each player

it must hold that Bj>

[15]

Aj+Dj

2

.

TABLE I

GENERAL PAYOFFS FOR THE PRISONER’S DILEMMA

Player 2 Cooperates

B1, B2

A1, D2

Player 2 Defects

D1, A2

C1, C2

Player 1 Cooperates

Player 1 Defects

Then, the game is said to be equivalent to a Prisoner’s

Dilemma type of game.

We prove next that the cooperative-neighbourhood game is

equivalent to a Prisoner’s Dilemma type of game by making

use of Table II, which illustrates the mapping between a unit’s

payoff in a cooperative-neighbourhood game and the payoffs

in a Prisoner’s Dilemma type of game.

TABLE II

THE MAPPING BETWEEN THE PAYOFFS FOR EITHER UNIT IN THE

COOPERATIVE-NEIGHBOURHOOD GAME AND THE PAYOFFS FOR EITHER

PLAYER IN THE PRISONER’S DILEMMA TYPE OF GAME

Unit Payoffs

β = f(x?)

α = f(x?)

β?= f(x)

α?= f(x)

A

B

C

D

Proposition 3.1: The

(Definition 1) is equivalent to a Prisoner’s Dilemma game.

Proof: By Definition 1 we immediately conclude that:

Observation 1: There are two possible actions for a unit:

(i) to participate in a neighbourhood in a cooperaive way,

cooperative-neighbourhoodgame

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and (ii) to defect from cooperation and not participate in the

neighbourhood.

Observation 1 combined with Definition 2 imply that the

actions of the players in the cooperative-neighbourhood game

match the actions of the players of a Prisoner’s Dilemma type

of game. In particular, Table II maps each unit’s payoffs, to

actions A,B,C,D, as defined in Definition 2. We proceed to

prove:

Lemma 3.1: Set A,B,C,D according to Table II. Then it

holds that A > B > C > D.

Proof: By Definition 1 it is true that α?≤ β?< α < β.

Since, β is mapped to A, α to B, β?to C and α?to D, then

the relatiosnhip A > B > C > D holds.

We now proceed to prove that:

Lemma 3.2: The cooperative-neighbourhood game satisfies

condition 2 of Definition 2.

Proof: To prove the claim we must prove that the reward

for cooperation is greater than the payoff for the described

situation, i.e. for each player it must hold that B >A+D

For each unit,

α >β + α?

2

.

2

.

(1)

Since α and β are quantifications of an experience with

little to no interference, then ? = β −α is a very small value,

as opposed to ζ = α − α?, which is a larger value since

the two values represent on the one hand the case of little

to no interference and on the other hand the case of great

interference in the experience. Therefore it must hold that:

2α − β > α?.

(2)

Observation 1, Lemma 3.1, and Lemma 3.2 together com-

plete the proof of Proposition 3.1.

The decision of what to do comes from the following rea-

soning: If a player believes that his opponent will cooperate,

then the best option is certainly to defect. If a player believes

that his opponent will defect, then by cooperating he takes the

risk of receiving the least payoff, thus the best option is again

to defect. Therefore, based on this reasoning, each player will

defect because it is the best option no matter what the opponent

chooses. However, this is not the best possible outcome of the

game for both. The best solution for both players would be to

cooperate and receive the second best payoff.

The desirable cooperative behaviour must be somehow

motivated so that the players’ selfish but rational reasoning

results in the cooperative decision. In fact, what we have

described is a one-shot Prisoner’s Dilemma, i.e. the players

have to decide only once – no previous or future interaction of

the two players affects this decision. Cooperation may evolve,

however, from playing the game repeatedly, against the same

opponent. This is referred to as Iterated Prisoner’s Dilemma,

which is based on a repeated game model with an unknown or

infinite number of repetitions2. The decisions at such games,

2The model of a repeated game has two kinds: the horizon may be finite,

i.e. it is known in how many periods the game ends, or infinite, i.e. the number

of game periods is unknown.

which are taken at each repetition of the game are affected by

past actions and future expectations, resulting in strategies that

motivate cooperation. In fact, the model of a repeated game

is designed to examine the logic of long-term interaction. It

captures the idea that a player will take into account the effect

of his current behaviour on the other player’s future behaviour.

The Iterated Prisoner’s Dilemma is a quite popular repeated

game model which demonstrates how cooperation can be

motivated by repetition (in the case the number of periods

is unknown), whereas in the one-shot Prisoner’s Dilemma as

well as in the finite version of the Iterated Prisoner’s Dilemma,

the two players are motivated to defect from cooperation. The

main idea is that if the game is played repeatedly, then the

mutually desirable cooperative outcome is stable because any

deviation will end the cooperation, resulting in a subsequent

loss for the deviating players that outweighs the payoff from

the finite horizon game (horizon of one or more periods).

A. Group strategy to motivate cooperation

In the scenario of a home wireless network deployment,

we may consider the interactions to be infinite, i.e. we have

no way of knowing if and when they will end. An additional

aspect that needs to be considered is the location of each unit,

which affects the group members it can select, i.e. the players

in the same neighbourhood that have strong enough signals to

support all terminals handled by the neighbourhood units. For

simplicity, we assume that each neighbourhood ideally forms a

separate group, i.e. all players in the neighbourhood cooperate

with each other and there are no partial coverage overlaps3.

We henceforth consider group strategies against defectors,

employing a “punishment” of a defector from a group, in

order to stregthen motivation to remain in a cooperative group.

It has been shown that group strategies can perform even

better than individual strategies known to prevail in a wide

range of cases, such as tit-for-tat [19]. We are inspired by the

Southampton group strategy [19], where members of a group

may assume one of two roles at any round of the game, and

furthermore, employ methods to recognise group members,

so that the strategy is “friendly” only towards own group

members. The Southampton strategy was the first strategy

to win against tit-for-tat strategy in the Prisoner’s Dilemma

tournament in 2004 [18]. It is a group strategy, employing

an identification mechanism that helps to distinguish group

members from opponent players. Particularly, in every inter-

action with another player, the Southampton player performs

a predetermined sequence of moves and uses the response of

the competing player to decide whether it is a member or not.

If the opponent is not also a Southampton player, the strategy

of the Southampton player is to keep defecting.

In the Southampton strategy an interaction of two players

where both employ the strategy leads to one of them defecting

and the other cooperating to increase the payoff of the group.

We propose a modified Southampton group strategy, where

3In fact it has been shown that in a Spatial Prisoner’s Dilemma type of

game, i.e. where many neighbourhoods are considered, the players may be

motivated again into a cooperative behaviour [15].

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if both players are in the same group then they should both

cooperate, since in our scenario the cost of a defection will

have a negative impact to the group (i.e. increase interference).

Two cooperating players, i.e. from the same group, may

assume different roles in the case that one of them is the leader

of the group and the other one is not, or have the same role

if none of them is the leader of the group. However, in both

cases we propose that the two players cooperate with each

other.

B. Repeated Interactions in Cooperative Neighbourhoods

This section briefly examines the numerical behaviour of

interacting players employing either the cooperative approach,

i.e. participate in a group and employ the modified Southamp-

ton strategy, or the defecting approach and do not participate

in the neighbourhood’s group, in fact defecting on each round.

The evaluation is based on a Matlab implementation of an iter-

ated Prisoner’s Dilemma type of game, where nine players (the

typical number for a single lattice used for a neighbourhood

in spatial Prisoner’s Dilemma games) interact either as coop-

erators or defectors. Thus, the strategies are played against

each other multiple times in order to evaluate the behaviour

of each strategy in terms of payoffs. The implementation of

the game model was based on a publicly available Matlab

implementation of the Iterated Prisoner’s Dilemma Game [20],

which has been modified to support the proposed version of

the Southampton strategy for the cooperative neighbourhood

game.

The implementation makes use of the following guidelines,

set to reflect the payoffs of the interaction game as shown

in Table II. In each simulation run, nine players play their

strategies and get payoffs accordingly. The numerical payoffs

are the following in a single round: if one player defects and

the other cooperates, the first gets 4 and the other gets 0, if

they both defect, each gets 2, and if they both cooperate each

gets 3. Eight different sets of simulations are run with the

first set of simulations considering that all nine neighbours

are members of the group and thus cooperators, the second

set of simulations assumes one defector in the neighbourhood,

the third set assumes two defectors and so on until the eight

simulation set which assumes seven defectors, i.e. the group

only has two members in the neighbourhood.

A randomly generated number of iterations was run repeat-

edly for each set of simulations to get cumulative payoffs for

each combination of strategies playing against each other. Note

that the strategies we have considered are the always-defect

strategy for the defector and the modified Southampton strat-

egy for the cooperator. The payoffs per strategy are eventually

added and averaged to give the average cooperator and the

average defector payoffs in each set of simulations, in order

to investigate the effect on the payoffs of the group members

as the number of defectors in a neghbourhood increase, given

the two particular strategies are used. The reason we generate

a random number of iterations in each simulation set, and get

the average, is to be able to include in our results behaviours

Fig. 1.

neighbourhood

Numerical results of interacting cooperators and defectors in a

that occur when the number of iterations is both small and

large.

Figure 1 shows the average cooperator and defector payoffs

in the eight different simulations sets. We observe that cooper-

ators enjoy overall higher payoffs than defectors, however, as

the defectors increase, the payoff of the group decreases and

thus the payoff per cooperating player decreases as well. This

makes sense since as defectors in a neighbourhood increase,

the interference increases and the quality of experience of

terminals in units participating in the cooperating group,

decreases. We may reach such conclusion by considering

the relationship between the payoffs used in the simulation

which matches the relationships between the payoffs in the

cooperative neighbourhood game.

IV. A PROTOCOL FOR COOPERATIVE NEIGHBOURHOODS

The equilibrium point of the cooperative neighbourhood

game, is that all members of a neighbourhood cooperate

by assuming either the role of the leader and serving all

terminals of the neighbourhood, or remaining silent to reduce

interference while its terminals are being served by the leader.

Therefore, based on the premise that there exists cooperation

between members of a particular neighbourhood, we next

outline a distributed protocol by specifying the interactions

between the neighbourhood members in terms of message

exchanges.

The protocol needs an identification phase so that an access

point may know its neighbourhood members. Let us primarily

consider the case that such a cooperative neighbourhood has

not been set up yet. The first step is to broadcast a request to

participate in the group. This is assumed to be a leadership

move, i.e. the initiator to form a group becomes the first leader

of the group (Figure 2). The cooperative members will respond

to the request by communicating a list of access points which

have strong signal to support their terminals and the leader

will find the common set of these lists with its own list and

broadcast the list of the final neighbourhood members. After

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Fig. 2. Initialization phase: requesting member becomes the leader

this phase each member of the group knows its neighbours.

Now, asymmetric cryptography can be used between the

members, i.e. the leader may communicate an encryption key,

to ensure that any further communication of session control

information is private within the neighbourhood.

In the case that the requesting member is not the initiator

of a group then the leader will respond with a message

identifying itself as a leader and including in the message

the list of group members and the encryption key for the

group (Figure 3). The rest of the neighbourhood members will

ignore the request if they are already participants of one of the

active cooperative neighbourhoods. The requesting member

needs to check whether it receives strong signal from all group

members and in case this is true, it responds with an OK to

the leader and the session information is then communicated

in a secure communication. The session is hence modified

by the leader so that the new neighbourhood member is

added. Otherwise, in the case the new member cannot join the

cooperative neighbourhood, it does not respond to the leader

and after a preset time interval elapses, the leader considers

this as a No response.

Once the identification phase is completed and the session

is set up or modified, each access point behaves in either of

two ways, serves all terminals in a neighbourhood or remains

silent. The rotation phase of the protocol occurs in a timely

manner according to the member number of each participant,

by a session modification initiated by the leader. Figure 2 and

Figure 3 show schematics of the setup phase of this protocol in

the case that the requesting member becomes the leader and in

the case the requesting member joins an active neighbourhood.

V. CONCLUSIONS AND FUTURE WORK

The paper investigated the interactions between wireless

access points that operate in the same geographical region

without any coordination. Using a game-theoric model in-

spired by the repeated Prisoner’s Dilemma type of game, we

showed that the players are motivated to create alliances with

Fig. 3. Initialization phase: requesting member joins an active neighbourhood

their neighbours so as to serve their terminals jointly and in

a coordinated manner, leading to an equilibrium where all

neighbours act cooperatively. Our numerical results show the

value of the cooperation for the case of infinitely repeated

interactions, and we have outlined a protocol that can support

the necessary coordination and deals with cooperation requests

during the formation of a cooperative neighbourhood.

Our current model is limited by the approximation that

all players (access points) within a cooperative group are

perfectly equivalent and interchangeable, and can serve each

other’s terminals with equal performance. The extension of

the model and results to allow for more complex topologies

with partial neighbourhood relationships among the APs (i.e.

where ranges of the individual APs overlap only partially),

and their evaluation using a more realistic wireless networking

simulation environment, are the subject of ongoing work.

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