Social Behavior: Evolutionary Game Theory

Matrix (Discrete) Games

General Rules for SolvingExample: Hawk-Dove Game

Hypothesis: Fitness Increases with PayoffSolve: Evolutionarily Stable Strategy (ESS)

Game Theory

Economic Interaction2 or More (N) “Players”

Each Has Behavioral Strategy

Assume Each Player’s Behavior Affects Own and Other Player’s Fitness

Game Theory

Model for Competition, Mutualism, Reciprocity, Cooperation

Evolutionarily Stable Strategy If Common, Repels All Rare Mutants (Other Strategies)

ESS Theory

PopulationBehavior = 2 Alleles

A Common, B Rare

Can B Invade A?

If Not, A is an ESS

ESS Theory

A Common, B RareB Does Not Invade A

Pure A: Evolutionarily Stable

(Against B)

ESS Theory

A Common, B Rare

B Invades andExcludes A

A Does Not AdvanceWhen Rare

Pure B is an ESS

ESS Theory

A Common, B Rare

B Invades; A PersistsEquilibrium System

Mixed ESSPolymorphismIndividuals Mix

ESS Theory

Payoff Matrix

Payoff to PlayerControlling Rows

Discrete Game,Identical Players(Symmetric)

ESS Theory

Evolutionarily Stable Strategy

Payoff Matrix: Symmetric GamePayoff matrix: Player 1

Player 2 ActionA B

Player 1 A

Player 1 B

Finding ESS

Finding ESS

ESS: Find p*

ESS: Find p*

Bistable: 2 ESS frequencies,

p* = 0 AND p* = 1

Diversity Among Populations

ESS: Find p*

No Pure ESS; Mixed ESS

Diversity Within Populations