The Evolution of The Evolution of CooperationCooperation

Shade ShuttersShade Shutters

School of Life Sciences &School of Life Sciences &Center for Environmental StudiesCenter for Environmental Studies

Why Cooperation?Why Cooperation?

No true Darwinian explanationNo true Darwinian explanation

““The Tragedy of the Commons”The Tragedy of the Commons”

The prisoners’ dilemmaThe prisoners’ dilemma

Often a prerequisite for sustainabilityOften a prerequisite for sustainability

The Prisoners’ DilemmaThe Prisoners’ Dilemma

YOUconfess lie

conf

ess

1 year go free

lie 5 years 3 yearsA F

RIE

ND

Why Does Cooperation Exist?Why Does Cooperation Exist?

Theories of kin selectionTheories of kin selection

Theories of reciprocal altruismTheories of reciprocal altruism

Theories of non-reciprocal altruismTheories of non-reciprocal altruism– Riolo et al (2001)Riolo et al (2001)

The ModelThe Model

Proposed by Riolo et al (2001)Proposed by Riolo et al (2001)

Agent-basedAgent-based

Programmed in JAVAProgrammed in JAVA

Agent ParametersAgent Parameters

Each agent has only 3 variablesEach agent has only 3 variables

– Tag valueTag value

– Recognition ToleranceRecognition Tolerance

– FitnessFitness

Tag ValueTag Value

A generic trait detectable by othersA generic trait detectable by others

– Think of this as hair or eye colorThink of this as hair or eye color

– A value on [0, 1] and initially randomA value on [0, 1] and initially random

Recognition ToleranceRecognition Tolerance

A range around each agent’s Tag A range around each agent’s Tag valuevalue

– A measure of how likely an agent is to A measure of how likely an agent is to consider another agent “similar”consider another agent “similar”

– A value on [0, 1] and initially randomA value on [0, 1] and initially random

The 3 phases of a generationThe 3 phases of a generation

1) Pairings1) Pairings– Random, unidirectional meetings between agentsRandom, unidirectional meetings between agents– The initiating agent donates to the other if the other is The initiating agent donates to the other if the other is

deemed “similar” and is charged a costdeemed “similar” and is charged a cost

– FitnessFitnesst+1 t+1 = Fitness= Fitnesstt + donations - costs + donations - costs

2) Matings2) Matings– Random meetings in which fitnesses are comparedRandom meetings in which fitnesses are compared– Agent with greater fitness enters next generationAgent with greater fitness enters next generation– Winners of ties are determined randomly (50/50)Winners of ties are determined randomly (50/50)

The 3 phases of a generationThe 3 phases of a generation

3) Random mutations3) Random mutations

– With a probability of With a probability of m, m, each agent destined each agent destined for the next generation mutatesfor the next generation mutates

– Mutation = Gaussian noise (Mutation = Gaussian noise (µµ = 0, = 0, σσ = 1) = 1) added to both the Tag and Toleranceadded to both the Tag and Tolerance

– Parameters knocked outside of [0, 1] by Parameters knocked outside of [0, 1] by mutation are adjusted back to either 0 or 1mutation are adjusted back to either 0 or 1

Pairing examplePairing example

Agent A (the selecting agent)Agent A (the selecting agent)– Tag = 0.54, Tolerance = 0.22Tag = 0.54, Tolerance = 0.22– Range of recognition = 0.54 Range of recognition = 0.54 ± 0.22 or [0.32, 0.76]± 0.22 or [0.32, 0.76]

Agent B (the selected agent)Agent B (the selected agent)– Tag = 0.38, Tolerance - irrelevantTag = 0.38, Tolerance - irrelevant

ResultResult– Agent A sees B as similar and donatesAgent A sees B as similar and donates

– FitnessFitnessAA = Fitness = FitnessAA – cost – cost

– FitnessFitnessBB = Fitness = FitnessBB + donation + donation

Expected outcomeExpected outcome

Those that donate for nothing in Those that donate for nothing in return should go extinctreturn should go extinct

Tolerance should evolve to 0Tolerance should evolve to 0

Donations should ceaseDonations should cease

Results of a typical runResults of a typical run

Simulation parametersSimulation parameters

100 agents per generation100 agents per generation

Each pairs with 3 other agentsEach pairs with 3 other agents

Each agent mates with 1 other agentEach agent mates with 1 other agent

30,000 generation per run30,000 generation per run

30 runs30 runs

Full simulation resultsFull simulation results

Average tolerance = 0.018Average tolerance = 0.018

Average donation rate = 0.737Average donation rate = 0.737

CriticismsCriticisms

Ratio of donation to cost was highRatio of donation to cost was high– Donation = 1.00, cost = 0.05Donation = 1.00, cost = 0.05– When cost > 0.50, donations go awayWhen cost > 0.50, donations go away

Dependent on tolerance being ≤Dependent on tolerance being ≤– Riolo: donate if |tagRiolo: donate if |tagAA – tag – tagBB| ≤ tolerance| ≤ tolerance

– When using strict <, donations go to 0When using strict <, donations go to 0

ConclusionConclusion

Cooperation is a largely unexplained Cooperation is a largely unexplained phenomenonphenomenon

Cooperation is essential to the Cooperation is essential to the sustainable management of common sustainable management of common pool resourcespool resources

Agent-based modelling is helping to Agent-based modelling is helping to explain cooperationexplain cooperation

If you’re still interested…If you’re still interested…

The Journal of Artificial Societies and Social The Journal of Artificial Societies and Social Simulations (on-line journal)Simulations (on-line journal)

– http://jasss.soc.surrey.ac.uk/jasss.htmlhttp://jasss.soc.surrey.ac.uk/jasss.html

Complexity and Ecosystem Management: Complexity and Ecosystem Management: The Theory and Practice of Multi-agent The Theory and Practice of Multi-agent Systems (edited volume)Systems (edited volume)

– Ed. by Marco JanssenEd. by Marco Janssen