Emergence of synchronization induced by the interplay between two prisoner's dilemma games with volunteering in small-world networks

TL;DR

This paper investigates how synchronization emerges between two prisoner's dilemma games with voluntary participation on small-world networks, revealing different synchronization types and the influence of coupling strength.

Contribution

It introduces the study of synchronization phenomena in coupled prisoner's dilemma games on small-world networks, highlighting the effects of coupling strength on synchronization and oscillation amplitude.

Findings

Three types of synchronization identified: partial, total, and complete.

Complete synchronization occurs at high coupling factors.

Coupling strength affects oscillation amplitude of cooperator density.

Abstract

We studied synchronization between prisoner's dilemma games with voluntary participation in two Newman-Watts small-world networks. It was found that there are three kinds of synchronization: partial phase synchronization, total phase synchronization and complete synchronization, for varied coupling factors. Besides, two games can reach complete synchronization for the large enough coupling factor. We also discussed the effect of coupling factor on the amplitude of oscillation of $cooperator$ density.