evolutionary game dynamics
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Evolutionary Game Dynamics. The greatest conceptual revolution in biology...the replacement of typological thinking by population thinking.

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Presentation Transcript
slide2
The greatest conceptual revolution in biology...the replacement of typological thinking by population thinking.
  • Ernst Mayr
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
replicator equations for n 2
Replicator equations for n=2:
  • Dominance
  • Bistability
  • stable coexistence
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 nature30
Rock-Scissors-Paper in nature
  • Escherichia coli (bacteria)
  • can produce colicin (toxic) and immunity protein
  • can produce only immunity
  • can produce neither nor
slide34
Replicator dynamics assumes clonal replication (like begets like)
  • other derivation from models of learning and imitation
imitation dynamics36
Imitation Dynamics
  • Piecewise replicator-like
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