How memory cost, switching cost, and payoff non-linearity affect the evolution of persistence

Abstract Cooperation is a behavior which is costly to the actor and beneficial for the recipient. While in one-shot game, cooperation is not favored by natural selection, in repeated interactions, cooperation can be favored by natural selection if cooperators cooperate conditionally. Previous studies have revealed that retaliation, (imitate the opponent's behavior) and persistence, (imitate its own behavior) can promote the evolution of cooperation. Here, it is considered that a player has to remember its own behavior in order to behave persistently, and that a less switching cost is imposed to a persistent player. In this paper, we incorporate these costs and reexamine the effect of persistence on the evolution of cooperation. We have revealed that when memory cost is present, behaving persistently is not beneficial for its evolution, and that when switching cost is present, the evolution of persistence is more likely. Additionally, we also investigate the evolution of persistence in the case where payoff is not linear.

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