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

TL;DR

This paper investigates how adopting different strategies against different opponents affects cooperation in well-mixed populations playing the prisoner dilemma, revealing that cooperation is maintained through an implicit punishment mechanism.

Contribution

It introduces a novel replacement rule in evolutionary dynamics that preserves cooperation and demonstrates the effects of synchronous versus asynchronous updates.

Findings

Mutual cooperation is never destroyed under the model.

Synchronous updates lead to dominance of cooperation.

Asynchronous updates maintain only initial mutual cooperations.

Abstract

Here we study the effects of adopting different strategies against different opponent instead of adopting the same strategy against all of them in the prisoner dilemma structured in well-mixed populations. We consider an evolutionary process in which strategies that provide reproductive success are imitated and players replace one of their worst interactions by the new one. We set individuals in a well-mixed population so that network reciprocity effect is excluded and we analyze both synchronous and asynchronous updates. As a consequence of the replacement rule, we show that mutual cooperation is never destroyed and the initial fraction of mutual cooperation is a lower bound for the level of cooperation. We show by simulation and mean-field analysis that for synchronous update cooperation dominates while for asynchronous update only cooperations associated to the initial mutual cooperations are maintained. As a side effect of the replacement rule, an "implicit punishment" mechanism comes up in a way that exploitations are always neutralized providing evolutionary stability for cooperation.