The Evolution of Cooperation Shade Shutters School of Life Sciences & Center for Environmental Studies

Why Cooperation?  No true Darwinian explanation  “The Tragedy of the Commons”  The prisoners’ dilemma  Often a prerequisite for sustainability

The Prisoners’ Dilemma

Why Does Cooperation Exist?  Theories of kin selection  Theories of reciprocal altruism  Theories of non-reciprocal altruism –Riolo et al (2001)

The Model  Proposed by Riolo et al (2001)  Agent-based  Programmed in JAVA

Agent Parameters  Each agent has only 3 variables –Tag value –Recognition Tolerance –Fitness

Tag Value  A generic trait detectable by others –Think of this as hair or eye color –A value on [0, 1] and initially random

Recognition Tolerance  A range around each agent’s Tag value –A measure of how likely an agent is to consider another agent “similar” –A value on [0, 1] and initially random

The 3 phases of a generation  1) Pairings –Random, unidirectional meetings between agents –The initiating agent donates to the other if the other is deemed “similar” and is charged a cost –Fitness t+1 = Fitness t + donations - costs  2) Matings –Random meetings in which fitnesses are compared –Agent with greater fitness enters next generation –Winners of ties are determined randomly (50/50)

The 3 phases of a generation  3) Random mutations –With a probability of m, each agent destined for the next generation mutates –Mutation = Gaussian noise (µ = 0, σ = 1) added to both the Tag and Tolerance –Parameters knocked outside of [0, 1] by mutation are adjusted back to either 0 or 1

Pairing example  Agent A (the selecting agent) –Tag = 0.54, Tolerance = 0.22 –Range of recognition = 0.54 ± 0.22 or [0.32, 0.76]  Agent B (the selected agent) –Tag = 0.38, Tolerance - irrelevant  Result –Agent A sees B as similar and donates –Fitness A = Fitness A – cost –Fitness B = Fitness B + donation

Expected outcome  Those that donate for nothing in return should go extinct  Tolerance should evolve to 0  Donations should cease

Results of a typical run

Simulation parameters  100 agents per generation  Each pairs with 3 other agents  Each agent mates with 1 other agent  30,000 generation per run  30 runs

Full simulation results  Average tolerance =  Average donation rate = 0.737

Criticisms  Ratio of donation to cost was high –Donation = 1.00, cost = 0.05 –When cost > 0.50, donations go away  Dependent on tolerance being ≤ –Riolo: donate if |tag A – tag B | ≤ tolerance –When using strict <, donations go to 0

Conclusion  Cooperation is a largely unexplained phenomenon  Cooperation is essential to the sustainable management of common pool resources  Agent-based modelling is helping to explain cooperation

If you’re still interested…  The Journal of Artificial Societies and Social Simulations (on-line journal) –  Complexity and Ecosystem Management: The Theory and Practice of Multi-agent Systems (edited volume) –Ed. by Marco Janssen