Evolution of Cooperation in Mobile Ad Hoc Networks Jeff Hudack (working with some Italian guy)

Evolutionary Game Theory Components – The Game – Interaction Model – Strategy Evolution Repeated game play using the interaction model Strategies evolve according to replicator dynamic Widely applicable: – Sociology: interaction among self-interested individuals in society – Biology: evolution of complex ecosystems – Physics: arrangement and interaction of particles – Computer Science: multi-agent systems with self-interested agents

Game Evolutionary Game Theory Mobile Ad Hoc Networks Interaction Model Strategy Evolution

Prisoners’ Dilemma Players choose between cooperation (C) and defection (D) Models a situation in which two players may not cooperate for mutual benefit B > A > C > D A, AC, B B, CD, D C C D D

PD Example Mutual cooperation is beneficial to both agents (certain payoff) However, (D, D) is the strong equilibrium strategy 2, 20, 3 3, 01, 1 C C D D

Mobile Ad Hoc Networks Self-interested devices, want – to have their own packets forwarded – to conserve power Assumptions – All packets are of the same value and a neighbor will be punished for not forwarding any of them – Neighbors can be monitored to see their action and total payoff

Direct vs. Indirect Packets A DCB In a purely selfish scenario B does not care about A’s packets and will not punish C if he drops them To simplify the game we assume that B will punish C for dropping any packets, regardless of origin

Reduced PD (Nowak, May; 1992) R = 1, T = b (b > 1), S = P = 0 Single parameter b, the benefit of defection (C, C) - all packets forwarded (D, C), (C, D) - exploitation (D, D) - packets dropped 1, 10, b b, 00, 0 C C D D

Game Evolutionary Game Theory Mobile Ad Hoc Networks Interaction Model Strategy Evolution Packet Forwarding

Interaction Model Random Geometric Graph – Nodes placed randomly in space – Interact if within (Euclidean) distance r Toroidal space to avoid border effects such as – Edge nodes have no packets to forward – Lower degree at edges – Mobility models tend to gather at center Agents play all neighbors at each time step

Mobility Model Random Waypoint Model – Each agent chooses a destination point at random, moves towards it – When arrived, choose new waypoint – The most popular mobile ad hoc network simulation model (but not perfect!) Parameters – v: velocity of agents – p: pause time (p=0)

Game Evolutionary Game Theory Mobile Ad Hoc Networks Interaction Model Strategy Evolution Packet Forwarding RGG with RWP

Strategy Evolution Replication by imitation Choose a neighbor j at random – If P i > P j, do nothing – Otherwise, adopt neighbors strategy with probability proportionate to how much better they did

Game Evolutionary Game Theory Mobile Ad Hoc Networks Interaction Model Strategy Evolution Packet Forwarding RGG with RWP Replication by Imitation

Expectations Brownian movement keeps agents relatively close to one another RWP inherently leads to constant changing of neighbors It should be harder for RWP (a more realistic model) to converge to cooperation

Experiments Parameters – Fixed: N = 1000, r = 1 – Variable: b, ρ = N/L 2 XP1: Density -> % cooperation convergence – Fixed b = 1.1, v = {0.001, 0.01} XP2: Comparison of Brownian and RWP models – Link Change Rate (LCR) - frequency of link generations/breaks – Link Duration (LD) - lifespan of links XP3: b vs. v -> % cooperation convergence – Fixed ρ = 1.3

XP1: Motivation Show the transition of evolution to cooperation w.r.t. density Brownian, v=0.01 Meloni, S., Buscarino, A., Fortuna, L., and Frasca, M. (2009). Effects of mobility in a population of prisoner’s dilemma players. pages 1–4.

XP1: Agent Density (v=0.001)

XP1: Interpretation Convergence to cooperation is still possible with RWP! However, RWP needs slower movement to counteract the volatility of the mobility model Is it because the dynamic models are inherently different?

XP2: Motivation Brownian model with v = 0.01, σ = 1.3, b = 1.1 always converges to full cooperation RWP model with same parameters converges to defection RWP model with v = has similar behavior as Brownian with v=0.01 GOAL: Compare the dynamic properties of the mobility models

XP2: Link Change Rate

XP2: Link Duration

XP2: Results Brownian (v=0.01) – LCR: – LD: RWP (v=0.001) – LCR: – LD: Conclusion: Not even close!

XP2: Interpretation The LCR and LD are not the reasons for the different behavior The must be a different dynamic, guessing something like “edge diversity” NEED METRIC: How often are agents that disconnect reconnecting to each other?

XP3: Motivation Show the relationship between velocity and the benefit of defection In progress! Had to restart due to an error with random seeding giving agents the same waypoint.

Future Work New mobility models – Gauss-Markov turning model – Squad-based movement New replicator dynamics Stochastic PD for direct vs indirect routing Pockets of cooperation are no longer collection of individuals, but rather a structure with changing individuals – This may be the “big idea” for dissertation