The replicator equation in stochastic spatial evolutionary games

Yu-Ting Chen

Stochastic Processes and their Applications, 2023, vol. 157, issue C, 94-139

Abstract: We study the multi-type stochastic evolutionary game with death–birth updating in expanding spatial populations of size N→∞. 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.

Keywords: Evolutionary games; Voter model; Coalescence; Almost exponentiality of hitting times; The replicator equation; The Wright–Fisher diffusion (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2022.11.013

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