Sorting out the effect of spatial structure on the emergence of cooperation

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Abstract
The positive effect on cooperation of the spatial structure of a population is currently regarded as a well established principle in evolutionary game theory. Since Nowak and May's report of a promotion of cooperation in the Prisoner's Dilemma, the most demanding binary game, many subsequent studies have supported this conclusion. Some recent results, however, seem to refute it. The present situation is that this question remains basically unresolved, as it has not been investigated systematically and with enough detail, considering different social dilemmas and rules for the update of strategies. Moreover, the time evolution of these models has hardly been studied, with the result that a convincing explanation of the effect of spatial structure is not available. We have addressed these issues to provide a complete picture of the effect of spatial structure on the evolution of cooperation, as well as the identification of the underlying dynamical mechanisms. We have found that spatial structure, in general, only promotes cooperation on coordination games, like Stag Hunt, and that the positive effect on Prisoner's Dilemma occurs only with a particular non-stochastic rule. We explain all these effects in terms of the local densities of each strategy and the structure of equilibria of the game. As a result, the asymmetry between the effects on coordination and anti-coordination games arises as a fundamental feature of these evolutionary models.

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