Spatial prisoner's dilemma game with volunteering in Newman-Watts small-world networks

TL;DR

This study explores a modified spatial prisoner's dilemma game with voluntary participation on Newman-Watts small-world networks, revealing how network structure influences cooperation dynamics and collective oscillations.

Contribution

It introduces a new evolutionary game model with voluntary participation and strategy mutation on small-world networks, highlighting the effects of network randomness on cooperation.

Findings

Agents participate more in small-world regions at low temptation

Intensive collective oscillations occur in more random network regions

Strategy mutation influences cooperation stability

Abstract

A modified spatial prisoner's dilemma game with voluntary participation in Newman-Watts small-world networks is studied. Some reasonable ingredients are introduced to the game evolutionary dynamics: each agent in the network is a pure strategist and can only take one of three strategies (\emph {cooperator}, \emph {defector}, and \emph {loner}); its strategical transformation is associated with both the number of strategical states and the magnitude of average profits, which are adopted and acquired by its coplayers in the previous round of play; a stochastic strategy mutation is applied when it gets into the trouble of \emph {local commons} that the agent and its neighbors are in the same state and get the same average payoffs. In the case of very low temptation to defect, it is found that agents are willing to participate in the game in typical small-world region and intensive collective oscillations arise in more random region.