leuven2

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