Phase transitions for rock-scissors-paper game on different networks

TL;DR

This paper investigates phase transitions in the rock-scissors-paper game across various networks using simulations and mean-field methods, revealing universal critical behavior and the limited role of clustering.

Contribution

It introduces a comprehensive analysis of phase transitions on different networks, highlighting the universality of critical exponents and the insignificance of clustering coefficient.

Findings

Three stationary states identified across all network types.

Clustering coefficient has negligible effect on global oscillations.

Critical behavior appears universal with consistent exponents.

Abstract

Monte Carlo simulations and dynamical mean-field approximations are performed to study the phase transitions in rock-scissors-paper game on different host networks. These graphs are originated from lattices by introducing quenched and annealed randomness simultaneously. In the resulting phase diagrams three different stationary states are identified for all structures. The comparison of results on different networks suggests that the value of clustering coefficient plays an irrelevant role in the emergence of a global oscillating phase. The critical behavior of phase transitions seems to be universal and can be described by the same exponents.