Instability in spatial evolutionary games

Abstract

We investigate the aspects that influence the instability of spatial evolutionary games, namely the Prisoner's Dilemma and the Snowdrift games. In this paper instability is defined as the proportion of strategy changes in the asymptotic period of the evolutionary process. The results show that with the Prisoner's Dilemma, when the level of noise present in the decision process is very low, the instability decreases as the synchrony rate decreases. With the Snowdrift this pattern of behavior depends strongly on the interaction topology and arises only for random and scale-free networks. However, for large noise values, the instability in both games depends only on the proportion of cooperators present in the population: it increases as the proportion of cooperators approaches 0.5. We advance an explanation for this behavior. © 2009 Springer Berlin Heidelberg.