  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.
