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  • Letter
  • Open Access

Mean-field interactions in evolutionary spatial games

Dmitriy Antonov1, Evgeni Burovski1, and Lev Shchur1,2

  • 1HSE University, 101000 Moscow, Russia
  • 2Landau Institute for Theoretical Physics, 142432 Chernogolovka, Russia

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Phys. Rev. Research 3, L032072 – Published 24 September, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L032072

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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Phys. Rev. Research 3, L032072– Published 24 September, 2021
  • Received 19 May 2021
  • Accepted 13 September 2021
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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