Promotion of cooperation by Hybrid Migration mechanisms in the Spatial Prisoner's Dilemma Game

Migration is an important factor in the Spatial Prisoners Dilemma Game. An appropriate migration mechanism can improve the level of cooperation in the system. A well-noted mechanism is success-driven migration. However, if individuals migrations are solely driven by payoff, small groups of the individuals may geographically gather into scattered clusters, resulting in the reduction of the cooperation level of the entire population. In this paper, we therefore investigate whether this problem can be resolved by respectively mixing the success-driven migration with two additional migration mechanisms to form two new hybrid migration mechanisms. The first means of hybridization is to mix with the Mean-payoff-driven migration, in which an individual migrates to its first-order neighboring site when its payoff is less than the mean payoff of the whole population. The second means is to mix with the Escaping-defector-driven migration, in which an individual migrates according to the number of defectors among its neighbors. We compare these two hybrid mechanisms with the original migration mechanism that combines the success-driven and random-driven migrations. The simulation results show that the hybrid mechanisms we proposed can effectively eliminate the betrayal clusters and the cooperation level of the system can noticeably be improved. The effect of improving the cooperation level is more significant in case that the initial population is sparse.