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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. C. D. C. D. - PowerPoint PPT Presentation
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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