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Spatial evolutionary games with weak selection.

Mridu Nanda1, Richard Durrett2

  • 1North Carolina School of Science and Mathematics, Durham, NC 27705.

Proceedings of the National Academy of Sciences of the United States of America
|May 24, 2017
PubMed
Summary
This summary is machine-generated.

Spatial game theory with weak selection can be analyzed using partial differential equations (PDEs). New rules predict the behavior of many spatial games by modifying their payoff matrices, sometimes leading to stable equilibria where PDEs alone do not.

Keywords:
bone cancercancer modelingpublic goods gamerock–paper–scissors

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Area of Science:

  • Evolutionary Game Theory
  • Mathematical Biology
  • Computational Social Science

Background:

  • A mathematical theory for spatial games with weak selection relies on convergence to partial differential equations (PDEs) under rescaling.
  • While applicable to many games, the behavior of limiting PDEs is unknown for certain classes of games.

Purpose of the Study:

  • To establish rules for predicting the behavior of a broad range of spatial games with weak selection.
  • To validate these predictive rules through computational simulations.

Main Methods:

  • Development of a theoretical framework linking spatial game dynamics to modified replicator equations.
  • Analysis of the effect of spatial structure as equivalent to alterations in the payoff matrix.
  • Validation using computer simulations of spatial games, including the rock-paper-scissors example.

Main Results:

  • A method is proposed to predict spatial game behavior by analyzing a modified replicator equation.
  • The effect of spatial structure is shown to be equivalent to modifying the game's payoff matrix.
  • In specific cases, like rock-paper-scissors, spatial effects can stabilize the system, leading to equilibrium outcomes not predicted by the standard replicator equation.

Conclusions:

  • The study provides a predictive framework for understanding spatial game dynamics with weak selection.
  • Spatial interactions can significantly alter evolutionary outcomes, stabilizing systems that would otherwise be unstable.
  • The findings offer insights into the role of spatial structure in shaping strategy evolution across various disciplines.