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Evolutionary Game Dynamics: A Conceptual Revolution in Biology

Explore the fascinating world of evolutionary game dynamics, from Nash equilibria to replicator equations and the folk theorem of evolutionary game theory. This concept revolutionizes typological thinking into population thinking and delves into the existence of Nash equilibria, dominance, bistability, and stable coexistence. Discover real-life examples like the 'Hawk-Dove' game and Rock-Scissors-Paper scenarios in nature. Dive into phase portraits, imitation dynamics, elimination of dominated strategies, best reply dynamics, and equilibrium selection in this illuminating field of study.

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Evolutionary Game Dynamics: A Conceptual Revolution in Biology

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  1. Evolutionary Game Dynamics

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

  3. Nash equilibria

  4. Nash equilibria

  5. Nash equilibria

  6. Symmetric Games

  7. Chicken Game

  8. John Maynard Smith

  9. Population setting

  10. Population setting

  11. Replicator equation

  12. Replicator equation

  13. Replicator equation

  14. Replicator equation

  15. Replicator dynamics and Nash equilibria

  16. Replicator dynamics and Nash equilibria

  17. 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

  18. Existence of Nash equilibria:

  19. Existence of Nash equilibria:

  20. Existence of Nash equilibria:

  21. Existence of Nash equilibria:

  22. Replicator equation for n=2

  23. Replicator equations for n=2: • Dominance • Bistability • stable coexistence

  24. Example dominance

  25. Example bistability

  26. Example coexistence

  27. The ‚Hawk-Dove‘ Game

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

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

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

  31. Rock-Scissors-Paper

  32. Rock-Scissors-Paper

  33. Phase portraits of Replicator equations:

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

  35. Imitation Dynamics

  36. Imitation Dynamics • Piecewise replicator-like

  37. Imitation Dynamics

  38. Imitation Dynamics

  39. Elimination of dominated strategies

  40. Elimination of dominated strategies

  41. Elimination of dominated strategies

  42. Best Reply Dynamics

  43. Best Reply Dynamics

  44. Best reply Dynamics

  45. Best reply Dynamics

  46. Best reply Dynamics

  47. Best reply Dynamics

  48. Adjustment Dynamics

  49. Adjustment Dynamics

  50. Equilibrium Selection

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