Diversity and critical behavior in prisoner's dilemma game

TL;DR

This paper investigates how network structure and game parameters influence cooperation in the prisoner's dilemma, revealing a critical percolation transition in complex, hierarchically organized networks.

Contribution

It introduces a model of PD on hierarchical scale-free networks with controllable shortcuts, identifying a percolation transition in cooperator clusters.

Findings

Cooperator clusters undergo a percolation transition in the (p,b) parameter space.

Cluster size distribution follows a power law at the transition point.

Network heterogeneity and stochastic dynamics drive critical social behavior.

Abstract

The prisoner's dilemma (PD) game is a simple model for understanding cooperative patterns in complex systems consisting of selfish individuals. Here, we study a PD game problem in scale-free networks containing hierarchically organized modules and controllable shortcuts connecting separated hubs. We find that cooperator clusters exhibit a percolation transition in the parameter space (p,b), where p is the occupation probability of shortcuts and b is the temptation payoff in the PD game. The cluster size distribution follows a power law at the transition point. Such a critical behavior, resulting from the combined effect of stochastic processes in the PD game and the heterogeneous structure of complex networks, illustrates the diversity of social relationships and the self-organization of cooperator communities in real-world systems.