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Mixing protocols in the public goods game.

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Network structure significantly impacts cooperation in social dilemma games. Even on a lattice, specific mixing frequencies can lead to well-mixed conditions, promoting cooperation through cluster formation.

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Area of Science:

  • Evolutionary game theory
  • Computational social science
  • Network science

Background:

  • Partner selection in social dilemmas profoundly affects evolutionary dynamics.
  • Random interactions lead to well-mixed populations, hindering cooperation mechanisms like network reciprocity.
  • Structured populations, via lattices or networks, allow cooperators to form protective clusters against defectors.

Purpose of the Study:

  • To investigate the conditions under which lattice-based mixing approximates well-mixed population dynamics in social dilemmas.
  • To analyze the influence of different mixing protocols (nearest-neighbor vs. random) and their frequencies on evolutionary outcomes.
  • To understand the relationship between cooperator cluster size and its fraction within the population.

Main Methods:

  • Simulations of the public goods game on a square lattice.
  • Implementation and comparison of nearest-neighbor mixing, random mixing, and hybrid protocols at varying frequencies.
  • Analysis of cooperator cluster size as a function of cooperator fraction and mixing parameters.

Main Results:

  • Nearest-neighbor mixing requires higher frequencies than random mixing to achieve well-mixed conditions.
  • Differences between mixing protocols are most pronounced at intermediate frequencies, converging at low and high frequencies.
  • A near-universal exponential growth in cooperator cluster size was observed as their fraction increased.

Conclusions:

  • Lattice mixing can lead to well-mixed conditions, but the required frequency depends on the mixing protocol.
  • Cooperator cluster size exhibits predictable growth patterns, offering insights into cooperation dynamics in structured populations.
  • Findings highlight the nuanced interplay between network structure, interaction rules, and the evolution of cooperation.