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Structural symmetry in evolutionary games.

Alex McAvoy1, Christoph Hauert2

  • 1Department of Mathematics, University of British Columbia, Vancouver, Canada V6T 1Z2 alexmcavoy@gmail.com.

Journal of the Royal Society, Interface
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Summary
This summary is machine-generated.

Evolutionary game theory defines homogeneity for invasion success in structured populations. Asymmetric games can be simplified to symmetric ones if the population structure is sufficiently symmetric.

Keywords:
evolutionfinite populationgame theory

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Area of Science:

  • Evolutionary Game Theory
  • Mathematical Biology
  • Population Dynamics

Background:

  • In evolutionary game theory, mutant strategy success is typically measured by fixation probability.
  • Fixation probability in structured populations can be location-dependent and is only one measure of success (e.g., fixation time is another).

Purpose of the Study:

  • To define and investigate the concept of homogeneity in evolutionary games, focusing on evolutionary equivalence of mutant states.
  • To determine conditions for homogeneity in evolutionary matrix games on graph-structured populations.
  • To explore the reduction of asymmetric games to symmetric games in structured populations.

Main Methods:

  • Definition of evolutionary equivalence for single-mutant states.
  • Analysis of asymmetric games to characterize homogeneity of the evolutionary process.
  • Derivation of precise conditions for homogeneity in evolutionary matrix games on graphs.

Main Results:

  • Introduced a notion of homogeneity applicable to the overall evolutionary process, not just population structure.
  • Identified conditions under which evolutionary matrix games on graph-structured populations are homogeneous.
  • Demonstrated that asymmetric matrix games can be reduced to symmetric games given sufficient population structure symmetry.

Conclusions:

  • Homogeneity is a property of the evolutionary process, encompassing various measures of mutant success.
  • Sufficient symmetry in population structure can simplify the analysis of asymmetric evolutionary games.
  • The framework provides a more comprehensive understanding of mutant invasion dynamics in structured populations.