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.