The effect of finite population size on the evolutionary dynamics in multi-person Prisoner's Dilemma

We study the influence of stochastic effects due to finite population size in the evolutionary dynamics of populations interacting in the multi-person Prisoner's Dilemma game. This paper is an extension of the investigation presented in a recent paper [Eriksson and Lindgren (2005), J. Theor. Biol. 232(3), 399]. One of the main results of the previous study is that there are modes of dynamic behaviour, such as limit cycles and fixed points, that are maintained due to a non-zero mutation level, resulting in a significantly higher level of cooperation than was reported in earlier studies. In the present study, we investigate two mechanisms in the evolutionary dynamics for finite populations: (i) a stochastic model of the mutation process, and (ii) a stochastic model of the selection process. The most evident effect comes from the second extension, where we find that a previously stable limit cycle is replaced by a trajectory that to a large extent is close to a fixed point that is stable in the deterministic model. The effect is strong even when population size is as large as 10,000. The effect of the first mechanism is less pronounced, and an argument for this difference is given.