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Evolutionary Games and Population Dynamics

Evolutionary Games and Population Dynamics. Oskar Morgenstern (1902-1977) John von Neumann (1903-1957) John Nash (b. 1930). Nash-Equilibrium. Arbitrarily many players each has arbitrarily many strategies there always exists an equilibrium solution no player can improve payoff by deviating

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Evolutionary Games and Population Dynamics

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  1. Evolutionary Games and Population Dynamics

  2. Oskar Morgenstern (1902-1977)John von Neumann (1903-1957)John Nash (b. 1930)

  3. Nash-Equilibrium • Arbitrarilymanyplayers • eachhasarbitrarilymanystrategies • therealwaysexists an equilibriumsolution • noplayercanimprovepayoffbydeviating • eachstrategybestreplytotheothers

  4. Nash equilibria can be ‚inefficient‘

  5. John Maynard Smith (1920-2004)

  6. Evolutionary Game Theory • Population ofplayers (not necessarily rational) • Subgroups meetandinteract • Strategies: Typesofbehaviour • Successfulstrategiesspread in population

  7. Population setting

  8. Population Dynamics

  9. Example: Moran Process

  10. Discrete time

  11. Continuous time

  12. Replicator Dynamics

  13. Replicator dynamics and Nash equilibria

  14. Replicator equation

  15. Replicator equation for n=2

  16. Replicator equation for n=2 • Dominance • Bistability • stable coexistence

  17. Example dominance

  18. Vampire Bat (Desmodus rotundus)

  19. Vampire Bat (Desmodus rotundus)

  20. Vampire Bats Blood donation as a Prisoner‘s Dilemma? Wilkinson, Nature 1990 The trait should vanish Repeated Interactions? (or kin selection?)

  21. Example bistability

  22. Example bistability

  23. Example coexistence

  24. Example coexistence

  25. Innerspecific conflicts Ritual fighting Konrad Lorenz: …arterhaltende Funktion

  26. Maynard Smith and Price, 1974:

  27. Example neutrality

  28. If n=3 strategies • Example: Rock-Paper-Scissors

  29. Rock-Paper-Scissors

  30. Rock-Paper-Scissors

  31. Generalized Rock-Paper-Scissors

  32. Generalized Rock-Paper-Scissors

  33. Bacterial Game Dynamics • Escherichia coli • Type A: wild type

  34. Bacterial Game Dynamics • Escherichia coli • Type A: wild type • Type B: mutant producing colicin (toxic) and an immunity protein

  35. Bacterial Game Dynamics • Escherichia coli • Type A: wild type • Type B: mutant producing colicin (toxic) and an immunity protein • Type C: produces only the immunity protein

  36. Bacterial Game Dynamics • Escherichia coli • Rock-Paper-Scissors cycle • Not permanent! • Serial transfer (from flask to flask): • only one type can survive! • (Kerr et al, Nature 2002)

  37. Mating behavior • Uta stansburiana (lizards) • (Sinervo and Lively, Nature, 1998)

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