Random partnerships in spatial game theory

Abstract

We study the effects of random partnerships, introduced to interaction or replacement networks, on the evolution of cooperation in spatial game theory on a square lattice. For the spatial prisoner dilemma game, we show that, compared with the case without random partnership, cooperation can be enhanced regardless of whether a random partnership is introduced to an interaction or replacement network. Specifically, the enhancement of cooperation is strongest in the limit of zero randomness. We show explicitly that the cooperator frequency is a decreasing function of randomness, and the cooperation eventually vanishes once the randomness is strong enough. For the spatial snow drift game, we find that the enhancement of cooperation occurs only when a random partnership is introduced to an interaction network.