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The replicator equation in stochastic spatial evolutionary games

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  • Chen, Yu-Ting

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.

Suggested Citation

  • Chen, Yu-Ting, 2023. "The replicator equation in stochastic spatial evolutionary games," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 94-139.
    • Handle: RePEc:eee:spapps:v:157:y:2023:i:c:p:94-139
    DOI: 10.1016/j.spa.2022.11.013
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    References listed on IDEAS

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