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arXiv · 2010.06025

The replicator equation in stochastic spatial evolutionary games

Yu-Ting Chen
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Abstract

We study the multi-strategy stochastic evolutionary game with death-birth updating in expanding spatial populations of size $N\to \infty$. The model is a voter model perturbation. For typical populations, we require perturbation strengths satisfying $1/N\ll w\ll 1$. Under appropriate conditions on the space, the limiting density processes of strategy are proven to obey the replicator equation, and the normalized fluctuations converge to a Gaussian process with the Wright-Fisher covariance function in the limiting densities. As an application, we resolve in the positive a conjecture from the biological literature that the expected density processes approximate the replicator equation on many non-regular graphs.

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Yu-Ting Chen. 2020-10-12. The replicator equation in stochastic spatial evolutionary games. https://arxiv.org/abs/2010.06025

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