Evolutionary cycles of cooperation and defection

Lorens A. Imhof · Drew Fudenberg · Martin A. Nowak

380 citations0/0 files storedProceedings of the National Academy of Sciences

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Evolutionary Game Theory and Cooperation Evolution and Genetic Dynamics Game Theory and Applications

Abstract

The main obstacle for the evolution of cooperation is that natural selection favors defection in most settings. In the repeated prisoner's dilemma, two individuals interact several times, and, in each round, they have a choice between cooperation and defection. We analyze the evolutionary dynamics of three simple strategies for the repeated prisoner's dilemma: always defect (ALLD), always cooperate (ALLC), and tit-for-tat (TFT). We study mutation-selection dynamics in finite populations. Despite ALLD being the only strict Nash equilibrium, we observe evolutionary oscillations among all three strategies. The population cycles from ALLD to TFT to ALLC and back to ALLD. Most surprisingly, the time average of these oscillations can be entirely concentrated on TFT. In contrast to the classical expectation, which is informed by deterministic evolutionary game theory of infinitely large populations, stochastic evolution of finite populations need not choose the strict Nash equilibrium and can therefore favor cooperation over defection.

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References

1981The Evolution of Cooperation 1971The Evolution of Reciprocal Altruism 1988Evolution and the Theory of Games 1950Equilibrium points in n -person games 1998Evolutionary Games and Population Dynamics 2015Games and Decisions 1978Evolutionary stable strategies and game dynamics 1986The Folk Theorem in Repeated Games with Discounting or with Incomplete Information

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