Stochastic Stability and Disagreements Between Dynamics

The replicator dynamics and Moran process are the main deterministic and stochastic models of evolutionary game theory. These models are connected by a mean-field relationship—the former describes the expected behavior of the latter. However, there are conditions under which their predictions diverge. I demonstrate that the divergence between their predictions is a function of standard techniques used in their analysis, and of differences in the idealizations involved in each. My analysis reveals problems for stochastic stability analysis in a broad class of games. I also demonstrate a novel domain of agreement between the dynamics, and draw a broader methodological moral for evolutionary modeling.