Social Behavior: Evolutionary Game Theory

Social Behavior: Evolutionary Game Theory Matrix (Discrete) Games General Rules for Solving Example: Hawk-Dove Game Hypothesis: Fitness Increases with Payoff Evolutionarily Stable Strategy (ESS)

Game Theory Economic Interaction 2 or More (N) “Players” Each Has Behavioral Strategy: Phenotype Social: Assume Each Player’s Behavior Affects Own and Other Player’s Fitness

Game Theory Model for Competition, Mutualism, Reciprocity, Cooperation Single “Round,” Repeated Play ESS:Evolutionarily Stable Strategy If Common, Repels All Rare Mutants (Other Strategies)

ESS Theory Population Behavior = Allele A Common, B Rare Can B Invade A? If Not, A is an ESS

ESS Theory: Monomorphic A Common, B Rare B Does Not Invade A Pure A: Evolutionarily Stable (Against B) Monomorphism: No Diversity at Equilibrium

ESS Theory: Monomorphic A Common, B Rare BInvades and ExcludesA A Does Not Advance When Rare Pure B is an ESS

ESS Theory: Polymorphic A Common, B Rare B Invades; A Persists Equilibrium System Mixed ESS Polymorphism Individuals Mix Behavioral Diversity Stable

ESS Theory: 2 Players Payoff Matrix Payoff to Player Controlling Rows Discrete Game, Identical Players (Symmetric)

ESS Theory

Payoff Matrix: Symmetric Game 2 Behaviors (A and B) Individuals Interact as Random Pairs

Finding ESS

Finding ESS Payoffs: Frequency-dependent p Frequency of A; 0  p  1 (1 – p) Frequency of B Payoffs EA, EB functions of p

Frequency Dependence Play A or Play B EA = p E(A,A) + (1 - p) E(A,B) EB = p E(B,A) + (1 - p) E(B,A) Linear in frequency of A

Frequency Dependence EA = p (4) + (1 - p) 3 EB = p (2) + (1 - p) 1 Plot; A Always Better Choice

Frequency-Dependence Mixed ESS; Bistable ESS

Social Behavior: Evolutionary Game Theory