Collective chasing behavior between cooperators and defectors in the spatial prisoner's dilemma

Random migration with tie retention promotes cooperation in the prisoner's dilemma game

Migration has the potential to induce outbreaks of cooperation, yet little is known about random migration. Does random migration really inhibit cooperation as often as previously thought? Besides, prior literature has often ignored the stickiness of social ties when designing migration protocols and assumed that players always immediately disconnect from their ex-neighbors once they migrate. However, this is not always true. Here, we propose a model where players can still retain some bonds with their ex-partners after they move from one place to another. The results show that maintaining a certain number of social ties, regardless of prosocial, exploitative, or punitive, can nevertheless facilitate cooperation even if migration occurs in a totally random fashion. Notably, it reflects that tie retention can help random migration, previously thought to be harmful to cooperation, restore the ability to spark bursts of cooperation. The maximum number of retained ex-neighbors plays an important role in facilitating cooperation. We analyze the impact of social diversity in terms of the maximum number of retained ex-neighbors and migration probability, and find that the former enhances cooperation while the latter often engenders an optimal dependence between cooperation and migration. Our results instantiate a scenario in which random migration yields the outbreak of cooperation and highlight the importance of social stickiness.

Spontaneous symmetry breaking in interdependent networked game

Spatial evolution game has traditionally assumed that players interact with direct neighbors on a single network, which is isolated and not influenced by other systems. However, this is not fully consistent with recent research identification that interactions between networks play a crucial rule for the outcome of evolutionary games taking place on them. In this work, we introduce the simple game model into the interdependent networks composed of two networks. By means of imitation dynamics, we display that when the interdependent factor α is smaller than a threshold value α(C), the symmetry of cooperation can be guaranteed. Interestingly, as interdependent factor exceeds α(C), spontaneous symmetry breaking of fraction of cooperators presents itself between different networks. With respect to the breakage of symmetry, it is induced by asynchronous expansion between heterogeneous strategy couples of both networks, which further enriches the content of spatial reciprocity. Moreover, our results can be well predicted by the strategy-couple pair approximation method.

Effect of initial fraction of cooperators on cooperative behavior in evolutionary prisoner's dilemma game

We investigate the influence of initial fraction of cooperators on the evolution of cooperation in spatial prisoner's dilemma games. Compared with the results of heterogeneous networks, we find that there is a relatively low initial fraction of cooperators to guarantee higher equilibrium cooperative level. While this interesting phenomenon is contrary to the commonly shared knowledge that higher initial fraction of cooperators can provide better environment for the evolution of cooperation. To support our outcome, we explore the time courses of cooperation and find that the whole course can be divided into two sequent stages: enduring (END) and expanding (EXP) periods. At the end of END period, thought there is a limited number of cooperator clusters left for the case of low initial setup, these clusters can smoothly expand to hold the whole system in the EXP period. However, for high initial fraction of cooperators, superfluous cooperator clusters hinder their effective expansion, which induces many remaining defectors surrounding the cooperator clusters. Moreover, through intensive analysis, we also demonstrate that when the tendency of three cooperation cluster characteristics (cluster size, cluster number and cluster shape) are consistent within END and EXP periods, the state that maximizes cooperation can be favored.