Evolution of Cooperation in Mobile Ad Hoc Networks

Jeff Hudack(working with some Italian guy)

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, A C, B

B, C D, 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, 2 0, 3

3, 0 1, 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

Packet Forwarding Game

• Mutual cooperation is great, all packets forwarded, but defecting saves power• Benefit of defection (b > 1)• (D, D) is a weak equilibrium

1, 1 0, b

b, 0 0, 0

C

C

D

D

Evolutionary Game Theory• Components

– The Game– Interaction Model– Replicator Dynamics

• 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

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

Strategy Evolution

• Replication by imitation• Choose a neighbor j at random– If Pi > Pj, do nothing– Otherwise, adopt neighbors strategy with

probability proportionate to how much better they did

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)

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/L2

• 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 = 0.001 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: 0.033– LD: 122.89

• RWP (v=0.001)– LCR: 0.0037– LD: 1249.8

• 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