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Here we study the effects of adopting different strategies against differentopponent instead of adopting the same strategy against all of them in theprisoner dilemma structured in well-mixed populations. We consider anevolutionary process in which strategies that provide reproductive success areimitated and players replace one of their worst interactions by the new one. Weset individuals in a well-mixed population so that network reciprocity effectis excluded and we analyze both synchronous and asynchronous updates. As aconsequence of the replacement rule, we show that mutual cooperation is neverdestroyed and the initial fraction of mutual cooperation is a lower bound forthe level of cooperation. We show by simulation and mean-field analysis thatfor synchronous update cooperation dominates while for asynchronous update onlycooperations associated to the initial mutual cooperations are maintained. As aside effect of the replacement rule, an "implicit punishment" mechanism comesup in a way that exploitations are always neutralized providing evolutionarystability for cooperation.

Distinguishing the opponents in the prisoner dilemma in well-mixed populations