Effect of adaptive migration with interaction intensity on the evolution of cooperation

Migration (mobility) is a common natural phenomenon and a fundamental element in understanding population dynamics. Adaptive migration (Jiang et al., 2010) has been proposed as an important and efficient mechanism for the evolution of cooperation. In this paper, we focus on the effect of the adaptive migration on the evolution of cooperation by introducing interaction intensity, defined as a probability of the individual’s willingness to interact with an opponent. Our investigations are based on two game models, the Prisoner’s Dilemma game (PDG) and the Snowdrift game (SG). Our results indicate that this modified adaptive migration is much more advantageous for the evolution of cooperation over a larger range of the fraction of empty sites compared to the original adaptive migration mechanism. In moderately sparse populations, the evolution of cooperation can be facilitated through migration. Under this modified adaptive migration, cooperation thrives regardless of the type of game when sensitivity of the stimulus is high. Furthermore, compared to the PDG, the evolution of cooperation in the SG requires lower sensitivity. Finally, in both the PDG and the SG, this modified adaptive migration can induce an outbreak of cooperation in a defector-dominated environment. This reveals that under more efficient resource utilization – here meaning a low fraction of empty sites – modest migration encourages tighter connections between cooperators, which is more conducive to the evolution of cooperation.