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Multi-player games on the cycle.

Matthijs van Veelen1, Martin A Nowak

  • 1Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA. vanveelen@fas.harvard.edu

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Summary
This summary is machine-generated.

This study analyzes evolutionary game dynamics in multi-player games, comparing interactions on a cycle to well-mixed populations. Results reveal how strategy fixation probabilities differ across various game types and selection intensities.

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Area of Science:

  • Evolutionary Game Theory
  • Mathematical Biology
  • Computational Social Science

Background:

  • Multi-player games involve n individuals interacting and receiving payoffs.
  • Symmetric games feature payoffs dependent on strategy counts, not specific player configurations.
  • Interactions on a cycle involve n neighboring players.

Purpose of the Study:

  • To investigate fixation probabilities in stochastic evolutionary dynamics.
  • To derive analytical results for linear and exponential fitness on a cycle.
  • To compare cycle dynamics with well-mixed population models.

Main Methods:

  • Analysis of stochastic evolutionary dynamics.
  • Derivation of analytical results for fixation probabilities.
  • Comparison of cycle interactions versus well-mixed populations.

Main Results:

  • Analytical solutions for fixation probabilities on a cycle for linear and exponential fitness.
  • Quantification of differences between cycle and well-mixed population dynamics.
  • Demonstration of results for public goods, stag hunt, and snowdrift games.

Conclusions:

  • The spatial structure (cycle) significantly impacts evolutionary dynamics compared to well-mixed populations.
  • Analytical results provide insights into strategy evolution in finite populations.
  • Findings are applicable to understanding cooperation and competition in various multi-player scenarios.