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Area of Science:

  • Evolutionary Game Theory
  • Mathematical Biology
  • Network Science

Background:

  • The standard evolutionary death-birth protocol ignores focal player status in strategy updates.
  • Neighboring strategies are adopted based on fitness-proportional competition for vacant roles.

Purpose of the Study:

  • To generalize the death-birth protocol by incorporating a focal weight factor.
  • To analyze the impact of this weight factor on cooperation dynamics using evolutionary graph theory.

Main Methods:

  • Analysis of evolutionary graph theory on joint transitive graphs.
  • Introduction of a weight factor for comparing focal and invading neighbor payoffs.
  • Monte Carlo simulations on square lattices and verification across various network configurations.

Main Results:

  • Focal weight hinders cooperation under weak selection.
  • A critical tipping point for the weight factor was identified.
  • Cooperation becomes unattainable once the focal weight exceeds this tipping point.

Conclusions:

  • The focal weight factor significantly alters cooperation dynamics in evolutionary games.
  • The identified tipping point demonstrates a threshold beyond which cooperation collapses.
  • The findings are robust across different game structures and network topologies.