Game Theory, Evolutionary Stable Strategies

Transcript

1. Evolutionary Stable Strategies Budincsevity Norbert, 2016
2. Agenda • Interaction strategies • Evolutionary Stable Strategies • Cooperation • Altruism • Conclusion
3. Interaction strategies • Organisms interact to obtain resources • Antagonistic, cooperative, altruism • Interactions are costly • The energy spent is a cost to the organism, and the resources are benefits • Net gain or loss incurred by the organism = payoff
4. Game theory vs evolution
5. Evolutionarily stable strategies A strategy is said to be an evolutionary stable strategy (or ESS) if that strategy cannot be replaced, or invaded by any other strategy through natural selection.* Maynard Smith and Price specify two conditions for a strategy S to be an ESS. For all T≠S, either 1. E(S,S) > E(T,S), or 2. E(S,S) = E(T,S) and E(S,T) > E(T,T) *Smith, J. M. Evolution and the Theory of Games. Cambridge University Press, 1982. https://en.wikipedia.org/wiki/Evolutionarily_stable_strategy
6. Interaction as a game Hawk vs dove Game theory is based on the interactions of rational decision makers (humans) In evolutionary game theory the payoff is a surrogate for fitness and strategies evolve over many repeated iterations of the game Cowden, C. C. (2012) Game Theory, Evolutionary Stable Strategies and the Evolution of Biological Interactions. Nature Education Knowledge 3(10):6
7. Evolutionarily stable strategies A strategy is said to be an evolutionary stable strategy (or ESS) if that strategy cannot be replaced, or invaded by any other strategy through natural selection. Hawk vs dove example (The Selfish Gene by Richard Dawkins) Win = 50 points hawk, dove Defeat = O points dove Injury = -100 hawk Win but fight = -10 dove
8. ESS in this game 5/12 dove 7/12 hawk 2. Example: pirate vs fisher
14. Cooperation • Same two individuals will interact more than once (so called iterated prisoners' dilemma) • Hundreds to thousands of generations
15. Altruism • Altruism is most common in animals that exhibit social behavior • Warning calls or food sharing, and colony forming behavior • Likewise, a vampire bat that regurgitates its food to feed hungry bats will benefit from the same service when it is unable to find food* *Wilkinson, G. S. Reciprocal food sharing in the vampire bat. Nature 308, 181-184 (1984). doi:10.1038/308181a0 Trivers, R. L. Evolution of reciprocal altruism. Q. Rev. Biol. 46, 35-& (1971). doi:10.1086/406755
16. Complex Interactions • Pure or mixed strategy • Example for mixed strategy: avoid larger individuals and attack smaller individuals • Territorial fights, territories vary in quality • Ritualized combats • Bacteria that provide nitrogen the plant can use
17. Complex Interactions
18. Read more 1 Smith, J. M. Game theory and the evolution of behavior. Proc. R. Soc. Lond. Ser. B-Biol. Sci. 205, 475-488 (1979). 2 Axelrod, R. & Dion, D. The further evolution of cooperation. Science 242, 1385-1390 (1988). 3 Axelrod, R. & Hamilton, W. D. The evolution of cooperation. Science 211, 1390-1396 (1981). 4 Smith, J. M. Evolution and the Theory of Games. Cambridge University Press, 1982. 5 Taylor, P. D. & Jonker, L. B. Evolutionary stable strategies and game dynamics. Math. Biosci. 40, 145-156 (1978). 6 Crowley, P. H. Hawks, doves, and mixed-symmetry games. J. Theor. Biol. 204, 543-563 (2000).
19. Thanks for your attention!