Impact of separation of interaction and replacement neighborhoods on spatial reciprocity

Elucidating the evolution of cooperation is one of the greatest challenges in both evolutionary biology and social science. However, vast majority of existing studies simply assume that the interaction neighborhood and replacement neighborhood are symmetric, irrespective of the size of both neighborhoods. In this paper, we consider the asymmetrical setup, namely, the separation of interaction neighborhood and replacement neighborhood, into the prisoner’s dilemma game. In detail, it is assumed that there exist two types of players: player A possessing Moore interaction neighborhood and von Neumann replacement neighborhood and player B having von Neumann interaction neighborhood and Moore replacement neighborhood. Importantly, the fraction of former player is τ (the latter is 1 − τ), and this ration keeps constant during the whole process. By means of Monte Carlo simulations, it is unveiled that cooperation can be promoted to the highest level at middle τ, which is related to the formation of giant cluster. Moreover, we also inspect the impact of uncertainty on the phase diagrams and find that middle τ completely changes the evolution trend of low or middle value. It is thus suggested the separation of interaction and replacement neighborhoods may shed new light into the solution of social dilemmas.