Using Game Theory to Analyze Wireless Ad Hoc networks

1. Using Game Theory to Analyze Wireless Ad Hoc networks Vivek Srivastava March 24th 2004 Qualifier presentation

2. Outline Ad-Hoc + Game theory Game theory Ad-Hoc network Transport layer Network layer Social optimal Medium access layer Physical layer Future work Layered approach

3. Ad Hoc networks • What are ad hoc networks • Multi-hop communication • Reduced need for any infrastructure • Dynamic topology • Distributed, interactive stations • Ease of deployment • Potentially more robust to attack • Application of ad hoc networks • Military application • Disaster management • Impromptu communication between people

4. 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

5. Basic component B • 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 equilibrium • An action vector is a Nash equilibrium if and • An action vector from which no player can benefit by deviating unilaterally Confess Not confess A 5,5 0,15 Confess NE 15,0 1,1 Not confess Prisoner’s dilemma

6. Why game theory? • De-centralized nature of nodes • Independently adapting its operation based on perceived or measures statistics • Interactive decision makers • Decision taken by one node affects and influences the other nodes Game Component MANET Component Nodes in Network Player Set Available Adaptations Action Set Adaptation Algorithm Valuation Function (Preference Relations) Utility Function Decision Update Algorithm Learning Process

7. 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?

8. 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

9. Physical and Medium access layers • Power control • Adjust transmit power levels • Objective: To achieve a target signal-to-interference-to-noise ratio • Waveform adaptations • Selection of appropriate waveform to reduce interference • Involves the receiver of the signal to feedback the interference characteristics • No existing work that uses game theory • Medium access • Set the probability of packet transmission • Objective: To maximize individual throughput

10. 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

11. Network layer (Current research) • Node participation • Switch interfaces to a sleep state • Affects 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

12. 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

13. Transport layer • Analyze congestion control algorithms for selfish nodes [Shenker03] • Objective: Determine the optimal congestion window additive increase and multiplicative decrease parameters • Current 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

14. Summary • Game theory offers a promising set of tools to analytically model ad hoc networks • Game theory can be used • Analysis of ad hoc networks • Design of incentive mechanisms • Past research concentrated on wired/cellular networks • Design of robust protocols to deal with selfish behavior

15. 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

16. 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

17. 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.

18. 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.