Using Game Theory to Analyze Wireless Ad Hoc

networks

Vivek Srivastava

March 24th 2004

Qualifier presentation

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Outline

Ad-Hoc network Game theory Ad-Hoc + Game theory

Social optimalMedium access layer

Network layerTransport layer

Physical layer

Layered approachFuture work

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Ad Hoc networks What are ad hoc networks

Multi-hop communicationReduced need for any infrastructureDynamic topologyDistributed, interactive stationsEase of deploymentPotentially more robust to attack

Application of ad hoc networksMilitary applicationDisaster management Impromptu communication between people

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Game Theory Game theory – a branch of mathematics used

extensively in economics The study of mathematical models

of conflict and cooperation between

intelligent rational decision makers-Myerson (1991) Basic component: Game – A mathematical

representation of an interactive decision situation Important concepts

Conflict and cooperation Intelligent rational decision makers

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Basic component Strategic game – 3 basic components

A set of 2 or more players (N = {1,2,….n})A set of actions for each player ( )Utility function for every player ( )

Nash equilibriumAn action vector is a Nash equilibrium if and An action vector from which no player can benefit by deviating

unilaterally

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Prisoner’s dilemma

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Why game theory? De-centralized nature of nodes

Independently adapting its operation based on perceived or measures statistics

Interactive decision makersDecision taken by one node affects and influences the other

nodes

Available Adaptations

MANET Component Game Component

Action Set

Nodes in Network Player Set

Adaptation Algorithm

Decision Update Algorithm

Valuation Function(Preference Relations)

Utility Function

Learning Process

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Steps in application of game theory Develop a game theoretic model

Solution of game’s Nash equilibrium yields information about the steady state and convergence of the network

Does a steady state exist?Uniqueness of Nash equilibrium

Is it optimal? Do nodes converge to it? Is it stable? Does the steady state scale?

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Optimal equilibrium inducing mechanisms Credit exchange

Virtual currency [Buttyan01]

— Difficult to implement Reputation [Buchegger02]

— Appropriate for denial of service attacks Other schemes

Generous Tit-for-tat [Axelrod84]

— Node mimics the action of its peers

— Slightly generous Watchdog – pathrater mechanism [Marti00]

— Specific to prevent malicious/selfish behavior in routing Presence of centralized referee [MacKenzie01]

Not a player but an overseer Not a typical game theoretic scenario

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Physical and Medium access layers Power control

Adjust transmit power levelsObjective: To achieve a target signal-to-interference-to-noise ratio

Waveform adaptationsSelection of appropriate waveform to reduce interference Involves the receiver of the signal to feedback the interference

characteristicsNo existing work that uses game theory

Medium accessSet the probability of packet transmissionObjective: To maximize individual throughput

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Network layer (Research issues) Previous work restricted to analyzing selfish node

behavior while forwarding of packets Nodes decide on the proportion of packets/sessions to act as a

relay Energy is the main constraint “Selfishness is the only strategy that can naturally arise in a

single stage” (Assuming a repeated game) [Urpi03] [Srinivasan03]

Use of external incentive mechanisms to induce socially optimal equilibrium

Shortcomings Do not consider true ad hoc scenarios where nodes can

experience inherent trade-offs Do not consider mobility and influence on entire network Restrict the model to relaying packets

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Network layer (Current research) Node participation

Switch interfaces to a sleep stateAffects network operations

— Network partition— Network congestion

Individual benefits— Increased lifetime of nodes (inversely proportional)— Increase in throughput by participating (directly proportional)

Individual losses— Loss of information for an ongoing session— Overhead involved in discovering location of other nodes on

waking up— Extra flow of route queries due to frequent topology changes

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Network layer (Other issues) Malicious node behavior degrades performance of

dynamic source routing protocol [Marti00] Classic routing [Orda93]

Nodes decide on the amount of data to be sourced on shared paths to minimize the cost involved

Use of game theory – infant stage

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Transport layer Analyze congestion control algorithms for selfish nodes

[Shenker03]Objective: Determine the optimal congestion window additive

increase and multiplicative decrease parametersCurrent efforts restricted to traditional TCP congestion control

algorithms for wired networks

Ad hoc networks Incorporate the characteristics of the wireless medium in the

congestion control game

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Summary Game theory offers a promising set of tools to analytically

model ad hoc networks Game theory can be used

Analysis of ad hoc networksDesign of incentive mechanisms

Past research concentrated on wired/cellular networks Design of robust protocols to deal with selfish behavior

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Future Work Currently developing a model for node participation in an

ad hoc network Analyze the model using game theoretic techniques and

determine the optimal time a node should stay awake in the ad hoc network

Apply the node participation model to a well known routing protocol and study the effect of varying level of node participation

Incorporate mobility in the game theoretic model

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Written response Approach to solve the problem

Similar to Cournot oligopoly – strategy is “How much…?” Identical stations with identical benefit and cost functions

Simple model –applicable to a Aloha network Basic assumptions – Useful to provide the basic insight Not completely realistic Difficult to obtain social optimum in a distributed

environment of rational entities

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References [Akella02] A. Akella et al., “Selfish behavior and stability of Internet: A game theoretic analysis of

TCP,” Proceedings of ACM SIGCOMM Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications, August 2002, pp. 117-130.

[Axelrod84] Robert Axelrod, “The Evolution of Cooperation,” Basic Books, Reprint edition, New York, 1984.

[Buttyan01] L. Buttyan and J. P. Hubaux, “Nuglets: A virtual currency to stimulate cooperation in self organized mobile ad-hoc networks,” Swiss Federal Institute of Technology, Lausanne, Switzerland, Report no. DSC /2001/001, January 2001.

[Buchegger02] S. Buchegger and J.Y. Le Boudec, “Performance analysis of the CONFIDANT protocol: cooperation of nodes – fairness in dynamic ad-hoc networks,” Proceedings of ACM MobiHoc, June 2002.

[Felegyhazi03] M. Felegyhazi, L. Buttyan and J.-P. Hubaux, “Equilibrium analysis of packet forwarding strategies in wireless ad hoc networks – the static case,” Proceedings of IEEE Personal Wireless Communications, September 2003, pp. 776-789.

[Orda93] A. Orda, R. Rom and N. Shimkim, “Competitive routing in multi-user communication networks,” IEEE/ACM Transactions in Networking, vol. 1, no. 5, October 1993, pp. 510-521.

[MacKenzie01] A. B. MacKenzie and S.B. Wicker, “Selfish users in Aloha: a game theoretic approach,” Proceedings of Vehicular Technology Conference, vol. 3, October 2001, pp. 1354-1357.

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References [Marti00] S. Marti et. al, “Mitigating routing misbehavior in mobile ad hoc networks,” Proceedings

of Sixth Annual IEEE/ACM Intl. conference on Mobile Computing and Networking, April 2000, pp. 255-265.

[Srinivasan03] V. Srinivasan et al., “Cooperation in wireless ad hoc networks,” Proceedings of IEEE Infocom, vol.2, April 2003, pp. 808-817.

[Urpi03] A. Urpi, M. Bonuccelli and S. Giordano, “Modeling cooperation in mobile ad hoc networks: a formal description of selfishness,” Proceedings of the Workshop on Modeling and Optimization in Mobile and Wireless Ad Hoc networks, March 2003.