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

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EPFL, Lausanne, Switzerland Márk Félegyházi Outline Intro to ad hoc networks Problem formulation Related work Scenario – static case Analysis Simulation Conclusion Future work 2

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EPFL, Lausanne, Switzerland Márk Félegyházi Ad Hoc Networks 3 self-organizing network – no infrastructure each networking service is provided by the nodes themselves we focus on packet forwarding

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EPFL, Lausanne, Switzerland Márk Félegyházi Problem of cooperation 4 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]

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EPFL, Lausanne, Switzerland Márk Félegyházi Cooperation without incentives 5 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] SR3R1R2D session: energy class: energy class of the session two mechanisms: class distribution mechanism session acceptance mechanism

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EPFL, Lausanne, Switzerland Márk Félegyházi Static network scenario 6 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 network configuration specific conditions for cooperation s2 s1 s3

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EPFL, Lausanne, Switzerland Márk Félegyházi Modeling packet forwarding as a game 7 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) time 0time slot:1t cooperation level: p i (0)p i (1)p i (t)

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EPFL, Lausanne, Switzerland Márk Félegyházi Representation of the nodes as players 8 node i is represented as a machine M i Π is a multiplication gate corresponding the multiplicative feature of packet forwarding σ i represents the strategy of the node node i is playing against the rest of the network (represented by the box denoted by A -i )

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EPFL, Lausanne, Switzerland Márk Félegyházi Strategy of the nodes 9 strategy function for node i: example strategies: Strategy Function Initial cooperation level AllD (always defect) AllC (always cooperate) TFT (Tit-For-Tat) 0 1 1 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)

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EPFL, Lausanne, Switzerland Márk Félegyházi Concept of dependency graph 10 s2 s1 s3 s2 s1 s3 routes dependency graph dependency: the benefit of each source is dependent on the behavior of its forwarders dependency loop

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

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EPFL, Lausanne, Switzerland Márk Félegyházi Analytical Results (2) 12 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 where: ΔiΔi the length of the longest dependency loop G gain in one time slot if all traffic arrives at the destination C forwarding cost in one time slot if all traffic arrives at the destination ω discounting factor |F i | number of sources for node i L loss in one time slot if no traffic arrives at the destination s2 s1 s3 s2 s1 s3 routes dependency graph Corollary 2: If Theorem 3 holds for every node, it is a Nash-equilibrium.

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EPFL, Lausanne, Switzerland Márk Félegyházi Simulation Scenario 14 Number of nodes 100 Area type Torus Area size 1500 m x 1500 m Radio range 250 m Route length 4 hops Number of simulations 100 Confidence interval 95 %

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EPFL, Lausanne, Switzerland Márk Félegyházi Simulation Results 13 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

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EPFL, Lausanne, Switzerland Márk Félegyházi Conclusion 15 Model of packet forwarding in a static network using game theory Analytical results: 1.If everyone drops all packets, it is a Nash-equilibrium. 2.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.

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EPFL, Lausanne, Switzerland Márk Félegyházi Future work 16 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

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EPFL, Lausanne, Switzerland Márk Félegyházi Related work 17 [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.

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