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Structure coefficients and strategy selection in multiplayer games.

Alex McAvoy1, Christoph Hauert2

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

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|April 6, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces reducibility for multiplayer games, extending evolutionary game theory beyond two-player interactions. It develops new selection rules for complex games, crucial for understanding evolution in structured populations.

Keywords:
Evolutionary dynamicsFinite populationsGame theoryStochastic processesWeak selection

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Area of Science:

  • Evolutionary Game Theory
  • Mathematical Biology
  • Population Dynamics

Background:

  • Two-player games like Prisoner's Dilemma are well-studied in evolutionary game theory.
  • Multiplayer games and their evolutionary dynamics remain less explored, especially with multiple strategies.
  • Existing selection rules are limited to simpler game structures.

Purpose of the Study:

  • To introduce and define 'reducibility' for multiplayer games.
  • To extend selection rules (r-rules) to multiplayer games with multiple strategies.
  • To analyze irreducible games and their implications in structured populations.

Main Methods:

  • Developed a formal definition of reducibility for multiplayer games.
  • Extended existing selection rules to accommodate multiplayer, multi-strategy games.
  • Analyzed the growth of structure coefficients for symmetric games.

Main Results:

  • Introduced the concept of reducibility to connect multiplayer and two-player games.
  • Established new selection rules applicable to irreducible multiplayer games.
  • Demonstrated that structure coefficients grow polynomially with the number of players and strategies.
  • Included analysis of ecologically asymmetric games considering spatial positioning.

Conclusions:

  • Reducibility provides a framework for analyzing complex multiplayer games.
  • The extended selection rules are vital for understanding evolutionary dynamics in diverse game settings.
  • This work bridges a gap in evolutionary game theory, enabling broader applications.