Payoff-related migration enhances cooperation in the prisoner's dilemma game

In reality, migration of an individual usually correlates with the individual's financial or social status. Here, we consider the situation where migration of a player depends on the player's payoff to an evolutionary prisoner's dilemma game. When the mobility of a player is positively correlated with the player's normalized payoff, Pi, where the mobility of player i is defined as μi=Piα, we found that cooperation could be promoted strongly in the case of a high density of players because of the introduction of this kind of migration. Moreover, the system could reach a state of complete cooperation in a large region on the given parameter space. Interestingly, enhancement of cooperation shows a non-monotonic behavior with an increase in α. We also found that the positive effects of this kind of migration on cooperation are robust in the face of changes to the network structure and the strategy-updating rule. In addition, we consider another situation where the mobility of a player is anti-correlated with the player's normalized payoff, and we observe that cooperation enhancement still exists.