Synergistic effects of multi-games and migration on cooperation promotion

Both the multi-games and migration mechanism can enhance the cooperation, motivating us to explore their interaction. Thus, we incorporate the migration mechanism into multi-games for the first time to investigate the evolution of group cooperative behaviors. Groups on a network with vacant nodes are randomly divided into two types: those playing the Prisoner's Dilemma Game and those playing the Snowdrift Game, with each group free to randomly select either game for interactions. Migration follows a classic payoff-guided pattern, where individuals aim to maximize their payoffs. Specifically, before deciding to migrate, an individual's virtual payoff—defined as the cumulative payoff obtainable by moving to a given vacant node—is calculated. The individual's actual cumulative payoff is then compared to the maximum virtual payoff across all vacant nodes. If the former is lower, the individual migrates to the vacant node with the highest virtual payoff and imitates the strategy of the highest-payoff neighboring agent at the new location. Numerical simulations show that for a certain range of the temptation, almost all values of the magnitude of the sucker's payoff yield a high cooperation rate. When the vacancy rate is within a specific range, cooperative strategies dominate. Experimental results indicate that payoff matrix diversity and an appropriate vacancy rate can further synergistically promote cooperation. This new mechanism provides a novel perspective for understanding the emergence of group cooperative behaviors.