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