  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.
