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arXiv · 2107.11088

Mean-field interactions in evolutionary spatial games

Dmitriy Antonov·Evgeni Burovski·Lev Shchur
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Abstract

We introduce a mean-field term to an evolutionary spatial game model. Namely, we consider the game of Nowak and May, based on the Prisoner's dilemma, and augment the game rules by a self-consistent mean-field term. This way, an agent operates based on local information from its neighbors and nonlocal information via the mean-field coupling. We simulate the model and construct the steady-state phase diagram, which shows significant new features due to the mean-field term: while for the game of Nowak and May, steady states are characterized by a constant mean density of cooperators, the mean-field game contains steady states with a continuous dependence of the density on the payoff parameter. Moreover, the mean-field term changes the nature of transitions from discontinuous jumps in the steady-state density to jumps in the first derivative. The main effects are observed for stationary steady states, which are parametrically close to chaotic states: the mean-field coupling drives such stationary states into spatial chaos. Our approach can be readily generalized to a broad class of spatial evolutionary games with deterministic and stochastic decision rules.

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Dmitriy Antonov, Evgeni Burovski, Lev Shchur. 2021-07-23. Mean-field interactions in evolutionary spatial games. https://doi.org/10.1103/physrevresearch.3.l032072

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