Percolation in spatial evolutionary prisoner's dilemma game on two-dimensional lattices

Area of Science:

• Complex Systems
• Game Theory
• Statistical Physics

Background:

• The evolutionary prisoner's dilemma models cooperation and defection dynamics.
• Lattice structures influence spatial game outcomes.
• Percolation theory describes cluster formation and connectivity.

Purpose of the Study:

• Investigate spatial evolutionary prisoner's dilemma on different lattices.
• Analyze how lattice structure and game parameters affect cooperation and defection.
• Determine universality classes of observed percolation transitions.

Main Methods:

• Numerical analysis of the spatial evolutionary prisoner's dilemma game.
• Weak prisoner's dilemma with imitation max update rule.
• Finite-size scaling analysis for percolation transitions.

Main Results:

• Identified six regimes on triangular lattices, two on hexagonal, and three on square lattices.
• Cooperators percolate for small temptation values (b) on triangular lattices.
• Defectors percolate for large b across all studied lattices.
• All percolation transitions belong to the random percolation universality class.

Conclusions:

• Lattice coordination number significantly impacts percolation properties.
• Detailed cluster growth mechanisms define distinct regimes.
• The study provides a comprehensive understanding of spatial evolutionary games and percolation.