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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5,5 0,15
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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.