M árk Félegyh á zi

1. Equilibrium Analysis of Packet Forwarding Strategiesin Wireless Ad Hoc Networks – the Static Case Márk Félegyházi Jean-Pierre Hubaux Levente Buttyán {mark.felegyhazi, jean-pierre.hubaux}@epfl.ch buttyan@hit.bme.hu Laboratory for computer Communications and Applications, Swiss Federal Institute of Technology (EPFL) – Lausanne, Switzerland Laboratory of Cryptography and System Security, Budapest University of Technology and Economics TERMINODES Project (NCCR-MICS) http://www.terminodes.org 1

2. Outline • Intro to ad hoc networks • Problem formulation • Related work • Scenario – static case • Analysis • Simulation • Conclusion • Future work 2

3. Ad Hoc Networks • self-organizing network – no infrastructure • each networking service is provided by the nodes themselves • we focus on packet forwarding 3

4. Problem of cooperation Problem: If selfish nodes do not forward packets for others (do not cooperate with others), the network can be paralyzed. • Solution: Incentive for cooperation • virtual currency (nuglets): Nodes pay if they use a service and get paid if they contribute to the service. [ButtyanH03] • reputation system: Nodes maintain a belief about all nodes they have met. If a node is requesting a service, other nodes decide to provide it based on their belief about the requestor. [BucheggerLB02][MichiardiM03] 4

5. Cooperation without incentives Question: Do we need these incentive mechanisms or can cooperation exist based on the self-interest of the nodes? • Energy-efficient cooperation: Willingness to cooperate adapts to the energy class of the nodes. [SrinivasanNCR03] S R1 R2 R3 D session: energy class: energy class of the session two mechanisms: • class distribution mechanism • session acceptance mechanism 5

6. Static network scenario network configuration specific conditions for cooperation • static network • communication is based on multi-hop relaying • a communication chain is called a route • routes last for the whole duration of the game • each node is a source on only one route s1 s2 s3 6

7. Modeling packet forwarding as a game • time is slotted: nodes apply a decision for each time slot • nodes apply a decision for each route where they are relays • strategy is to define a cooperation level [0,1] for each time slot • source benefits if packets arrive • utility of the nodes is linear • rationality of the players: goal is to maximize utility • Utility: G*(number of packets arrived) – C*(number of packets transmitted) cooperation level: pi(0) pi(1) pi(t) time time slot: 0 1 t 7

8. Representation of the nodes as players • node i is represented as a machine Mi • Π is a multiplication gate corresponding the multiplicative feature of packet forwarding • σi represents the strategy of the node node i is playing against the rest of the network (represented by the box denoted by A-i) 8

9. Strategy of the nodes strategy function for node i: example strategies: Initial cooperation level Function Strategy 0 AllD (always defect) 1 AllC (always cooperate) 1 TFT (Tit-For-Tat) non-reactive strategies: the output of the strategy function is independent of the input (example: AllD and AllC) reactive strategies: the output of the strategy function depends on the input (example: TFT) 9

10. Concept of dependency graph dependency: the benefit of each source is dependent on the behavior of its forwarders s1 s1 dependency loop s2 s2 s3 s3 dependency graph routes 10

11. Analytical Results (1) Theorem 2: If a node has only non-reactive dependency loops, then its best strategy is AllD. Theorem 1: If a node does not have any dependency loops, then its best strategy is AllD. s1 If node s1 plays AllD: s1 s2 s2 s3 s3 Corollary 1: If every node plays AllD, it is a Nash-equilibrium. 11

12. where: gain in one time slot if all traffic arrives at the destination G loss in one time slot if no traffic arrives at the destination L forwarding cost in one time slot if all traffic arrives at the destination C discounting factor ω |Fi| number of sources for node i the length of the longest dependency loop Δi Analytical Results (2) • Theorem 3: The best strategy for node i is TFT, if: • Node i has a dependency loop with all of its sources, • the other nodes play TFT and • (G + L) ¢i > |Fi| ¢ C s1 s1 s2 s2 s3 s3 dependency graph routes Corollary 2: If Theorem 3 holds for every node, it is a Nash-equilibrium. 12

13. Simulation Scenario Number of nodes 100 Torus Area type Area size 1500 m x 1500 m Radio range 250 m Route length 4 hops Number of simulations 100 Confidence interval 95 % 14

14. Simulation Results • Theorem 3: The best strategy for node i is TFT, if: • Node i has a dependency loop with all of its sources, • the other nodes play TFT and • (G + L) ¢i > |Fi| ¢ C 13

15. Conclusion • Model of packet forwarding in a static network using game theory • Analytical results: • If everyone drops all packets, it is a Nash-equilibrium. • Given some conditions, there are Nash-equilibria, where all nodes forward all packets (i.e., everyone cooperates in the network). • Simulation results: The conditions for cooperative Nash-equilibria are very restrictive. In general, the likelihood that the conditions for cooperation hold for every node is extremely small. 15

16. Future work • Quantify the probability that all nodes cooperate in the network • The effect of the number of routes originating at each node • Possible equilibria that involve only a part of the nodes (local equilibria) • Consider a mobile scenario – impact of mobility • Emergence of cooperation 16

17. Related work [Axelrod84] - R. Axelrod, The Evolution of Cooperation, Basic Books, New York, 1984. [BucheggerLB02] – S. Buchegger, J-Y. Le Boudec, “Performance Analysis of the CONFIDANT Protocol (Cooperation Of Nodes--Fairness In Dynamic Ad-hoc NeTworks),” In Proc. 3rd ACM International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc'02), Lausanne, Switzerland, pp. 80-91, June 9-11, 2002. [ButtyanH03] – L. Buttyán, J.-P. Hubaux, “Stimulating Cooperation in Self-Organizing Mobile Ad Hoc Networks,” to appear in ACM/Kluwer Mobile Networks and Applications (MONET) Special Issue on Mobile Ad Hoc Networks, Vol. 8 No. 5, October 2003. [MichiardiM03] - P. Michiardi, R. Molva, “Core: A COllaborative REputation mechanism to enforce node cooperation in Mobile Ad Hoc Networks,” Communication and Multimedia Security 2002, Portoroz, Slovenia, September 26-27, 2002. [SrinivasanNCR03] - V. Srinivasan, P. Nuggehalli, C. Chiasserini, R. Rao, “Cooperation in Wireless Ad Hoc Networks,” In Proceedings of IEEE Infocom ‘03, San Francisco, USA, March 30- April 3, 2003. 17