Evolutionary Game Dynamics The greatest conceptual revolution in

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

Folk theorem of evolutionary game theory 4 Nash equilibria are rest points 4 strict

Replicator equations for n=2: 4 Dominance 4 Bistability 4 stable coexistence

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

Rock-Scissors-Paper in nature 4 Uta stansburiana (lizards) 4 males: 3 morphs (inheritable) 4 monogamous,

Rock-Scissors-Paper in nature 4 Escherichia coli (bacteria) 4 can produce colicin (toxic) and immunity

Phase portraits of Replicator equations:

4 Replicator dynamics assumes clonal replication (like begets like) 4 other derivation from models

Imitation Dynamics 4 Piecewise replicator- like

Equilibrium Selection via travelling waves

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Evolutionary Game Dynamics

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

Nash equilibria

Symmetric Games

Chicken Game

John Maynard Smith

Population setting

Replicator equation

Replicator dynamics and Nash equilibria

Folk theorem of evolutionary game theory 4 Nash equilibria are rest points 4 strict Nash equilibria are attractors 4 stable rest points are Nash equilibria 4 limits of interior orbits are Nash equilibria

Existence of Nash equilibria:

Replicator equation for n=2

Replicator equations for n=2: 4 Dominance 4 Bistability 4 stable coexistence

Example dominance

Example bistability

Example coexistence

The ‚Hawk-Dove‘ Game

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

Rock-Scissors-Paper in nature 4 Uta stansburiana (lizards) 4 males: 3 morphs (inheritable) 4 monogamous, guards female 4 polygamous, guards harem (less efficiently) 4 loose males, sneaky matings

Rock-Scissors-Paper in nature 4 Escherichia coli (bacteria) 4 can produce colicin (toxic) and immunity protein 4 can produce only immunity 4 can produce neither nor

Rock-Scissors-Paper

Phase portraits of Replicator equations:

4 Replicator dynamics assumes clonal replication (like begets like) 4 other derivation from models of learning and imitation

Imitation Dynamics

Imitation Dynamics 4 Piecewise replicator- like

Imitation Dynamics

Elimination of dominated strategies

Best Reply Dynamics

Best reply Dynamics

Adjustment Dynamics

Equilibrium Selection

Equilibrium Selection via travelling waves