Cooperation in noisy case: prisoner's dilemma game on two types of regular random graphs

TL;DR

This study investigates how noise and payoff variations influence cooperation in the prisoner's dilemma game on two types of random regular graphs, revealing phase transitions and optimal structures for cooperation.

Contribution

It introduces an analysis of cooperation dynamics on random regular graphs with different structures, highlighting the effects of noise and payoff on phase transitions.

Findings

System exhibits a second order phase transition from mixed to defector-only state.

Absence of loops enhances cooperation compared to square lattice.

Low noise favors optimal connectivity with randomly connected triangles.

Abstract

We have studied an evolutionary prisoner's dilemma game with players located on two types of random regular graphs with a degree of 4. The analysis is focused on the effects of payoffs and noise (temperature) on the maintenance of cooperation. When varying the noise level and/or the highest payoff, the system exhibits a second order phase transition from a mixed state of cooperators and defectors to an absorbing state where only defectors remain alive. For the random regular graph (and Bethe lattice) the behavior of the system is similar to those found previously on the square lattice with nearest neighbor interactions, although the measure of cooperation is enhanced by the absence of loops in the connectivity structure. For low noises the optimal connectivity structure is built up from randomly connected triangles.