Phase diagrams for Prisoner's Dilemma game on two-dimensional lattices

TL;DR

This paper investigates how payoffs and noise influence cooperation in the Prisoner's Dilemma on 2D lattices, revealing phase transitions and the importance of network structure for sustaining cooperation.

Contribution

It provides a systematic analysis of phase boundaries in the Prisoner's Dilemma on lattices using Monte Carlo simulations and mean-field approximations, highlighting the role of network connectivity.

Findings

Phase transition from mixed to defector-only state

Critical points depend on temperature and temptation

Cooperation persists only with certain network structures

Abstract

The effects of payoffs and noise on the maintenance of cooperative behavior are studied in an evolutionary Prisoner's Dilemma game with players located on the sites of different two-dimensional lattices. This system exhibits a phase transition from a mixed state of cooperators and defectors to a homogeneous one where only the defectors remain alive. Using systematic Monte Carlo simulations and different levels of the generalized mean-field approximations we have determined the phase boundaries (critical points) separating the two phases on the plane of the temperature (noise) and temptation to choose defection. In the zero temperature limit this analysis suggests that the cooperation can be sustained only for those connectivity structures where three-site clique percolation occurs.