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Evolutionary Game Dynamics: 

Evolutionary Game Dynamics

Slide2: 

The greatest conceptual revolution in biology...the replacement of typological thinking by population thinking. Ernst Mayr

Nash equilibria: 

Nash equilibria

Nash equilibria: 

Nash equilibria

Nash equilibria: 

Nash equilibria

Symmetric Games: 

Symmetric Games

Chicken Game: 

Chicken Game

John Maynard Smith: 

John Maynard Smith

Population setting: 

Population setting

Population setting: 

Population setting

Replicator equation: 

Replicator equation

Replicator equation: 

Replicator equation

Replicator equation: 

Replicator equation

Replicator equation: 

Replicator equation

Replicator dynamics and Nash equilibria: 

Replicator dynamics and Nash equilibria

Replicator dynamics and Nash equilibria: 

Replicator dynamics and Nash equilibria

Folk theorem of evolutionary game theory: 

Folk theorem of evolutionary game theory Nash equilibria are rest points strict Nash equilibria are attractors stable rest points are Nash equilibria limits of interior orbits are Nash equilibria

Existence of Nash equilibria:: 

Existence of Nash equilibria:

Existence of Nash equilibria:: 

Existence of Nash equilibria:

Existence of Nash equilibria:: 

Existence of Nash equilibria:

Existence of Nash equilibria:: 

Existence of Nash equilibria:

Replicator equation for n=2: 

Replicator equation for n=2

Replicator equations for n=2:: 

Replicator equations for n=2: Dominance Bistability stable coexistence

Example dominance: 

Example dominance

Example bistability: 

Example bistability

Example coexistence: 

Example coexistence

The ‚Hawk-Dove‘ Game: 

The ‚Hawk-Dove‘ Game

Replicator equations for n=3:: 

Replicator equations for n=3: Possibility for rock-scissors-paper heteroclinic cycles

Rock-Scissors-Paper in nature: 

Rock-Scissors-Paper in nature Uta stansburiana (lizards) males: 3 morphs (inheritable) monogamous, guards female polygamous, guards harem (less efficiently) loose males, sneaky matings

Rock-Scissors-Paper in nature: 

Rock-Scissors-Paper in nature Escherichia coli (bacteria) can produce colicin (toxic) and immunity protein can produce only immunity can produce neither nor

Rock-Scissors-Paper: 

Rock-Scissors-Paper

Rock-Scissors-Paper: 

Rock-Scissors-Paper

Phase portraits of Replicator equations:: 

Phase portraits of Replicator equations:

Slide34: 

Replicator dynamics assumes clonal replication (like begets like) other derivation from models of learning and imitation

Imitation Dynamics: 

Imitation Dynamics

Imitation Dynamics: 

Imitation Dynamics Piecewise replicator-like

Imitation Dynamics: 

Imitation Dynamics

Imitation Dynamics: 

Imitation Dynamics

Elimination of dominated strategies: 

Elimination of dominated strategies

Elimination of dominated strategies: 

Elimination of dominated strategies

Elimination of dominated strategies: 

Elimination of dominated strategies

Best Reply Dynamics: 

Best Reply Dynamics

Best Reply Dynamics: 

Best Reply Dynamics

Best reply Dynamics: 

Best reply Dynamics

Best reply Dynamics: 

Best reply Dynamics

Best reply Dynamics: 

Best reply Dynamics

Best reply Dynamics: 

Best reply Dynamics

Adjustment Dynamics: 

Adjustment Dynamics

Adjustment Dynamics: 

Adjustment Dynamics

Equilibrium Selection: 

Equilibrium Selection

Equilibrium Selection: 

Equilibrium Selection

Equilibrium Selection: 

Equilibrium Selection

Equilibrium Selection via travelling waves : 

Equilibrium Selection via travelling waves