Q-Strategy spatial prisonerʼs dilemma game

Abstract

We generalize the usual two-strategy prisonerʼs dilemma game to a multi-strategy game, in which the strategy variable s is allowed to take q different fractional values lying between 0 and 1. The fractional-valued strategies signify that individuals are not absolutely cooperative or defective, instead they can adopt intermediate strategies. Simulation results on 1D and 2D lattices show that, compared with the binary strategy game, the multi-strategy game can sustain cooperation in more stringent defective environments. We give a comprehensive analysis of the distributions of the survived strategies and we compare pairwise the relative strength and weakness of different strategies. It turns out that some intermediate strategies survive the pure defection because they can reduce being exploited and at the same time benefit from the spatial reciprocity effect. Our work may shed some light on the intermediate behaviors in human society.