The replicator equation in stochastic spatial evolutionary games

We study the multi-type stochastic evolutionary game with death-birth updating in expanding spatial populations of size N -> oo. The model is a voter model perturbation. For typical eligible populations, we require perturbation strengths satisfying 1/N << w << 1. Under these conditions, the main results prove that the vector density processes of type obey an extended replicator equation in the limit, and the normalized fluctuations converge to a Gaussian process subject to the Wright-Fisher covariance function. In particular, we obtain a positive resolution of a conjecture from [34] that the replicator equation extends to many non-regular graphs.Crown Copyright (c) 2022 Published by Elsevier B.V. All rights reserved.