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Jorge Peña1, Bin Wu1,2, Jordi Arranz1

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Evolutionary multiplayer games on graphs show that spatial structure can promote cooperation. However, complex graph structures like lattices can hinder cooperation more than well-mixed populations.

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Area of Science:

  • Evolutionary Game Theory
  • Mathematical Biology
  • Network Science

Background:

  • Evolutionary games are often studied in structured populations modeled as graphs.
  • Analytical results are limited to simpler games, with complex multiplayer games relying on simulations.

Purpose of the Study:

  • Investigate evolutionary multiplayer games on graphs using the Moran death-Birth process.
  • Derive analytical conditions for cooperation in structured populations.
  • Compare cooperation dynamics in structured versus well-mixed populations.

Main Methods:

  • Exact analytical solutions for cycles.
  • Pair and diffusion approximations for regular graphs (degree >= 3).
  • Computer simulations for validation on random regular graphs, cycles, and lattices.

Main Results:

  • An exact condition for cooperation on cycles was derived.
  • Approximations suggest structured populations generally promote cooperation.
  • Simulations validated approximations for random regular graphs and cycles.
  • Lattices showed more stringent conditions for cooperation than well-mixed populations.

Conclusions:

  • Pair approximation captures complexity in random graphs but requires caution for highly clustered graphs.
  • Spatial structure's impact on cooperation depends on graph topology.
  • Understanding graph structure is crucial for predicting evolutionary outcomes in multiplayer games.