The ambivalent effect of lattice structure on a spatial game

The evolution of cooperation is studied in lattice-structured populations, in which each individual who adopts one of the following strategies ‘always defect’ (ALLD), ‘tit-for-tat’ (TFT), and ‘always cooperate’ (ALLC) plays the repeated Prisoner’s Dilemma game with its neighbors according to an asynchronous update rule. Computer simulations are applied to analyse the dynamics depending on major parameters. Mathematical analyses based on invasion probability analysis, mean-field approximation, as well as pair approximation are also used. We find that the lattice structure promotes the evolution of cooperation compared with a non-spatial population, this is also confirmed by invasion probability analysis in one dimension. Meanwhile, it also inhibits the evolution of cooperation due to the advantage of being spiteful, which indicates the key role of specific life-history assumptions. Mean-field approximation fails to predict the outcome of computer simulations. Pair approximation is accurate in two dimensions but fails in one dimension.