Interactive diversity promotes cooperation in multi-games

In game theory, it is an important topic to study the emergence and maintenance of group cooperative behavior based on evolutionary game and complex network. However, in-depth analysis of cooperative behavior persistence becomes a significant challenge due to the betrayal induced by the temptation of high payoff and the difficulty of cooperation under high social dilemmas. Recent studies show that mixed strategy games and multi-game mechanics can greatly improve the ability of individuals with interactive diversity to resist temptation. In our study, we employ a model that integrates the Prisoner’s Dilemma (PD) and Snowdrift (SD) games, allowing players to engage in different types of games with their neighbors, thereby creating a more stable cooperative environment. The concept of the memory step enables players to maintain their strategies over a certain number of moves. When combined with the side-game mechanism, this significantly bolsters resistance to betrayal and encourages cooperative behavior. Numerical simulations were conducted to uncover the impact of the memory step and the sucker’s payoff on the evolution of cooperation, and to identify the optimal threshold for the memory step. This threshold balances the trade-off between cooperation and defection. The findings suggest that interactive diversity, facilitated by strategic memory steps and side-games, can effectively alleviate social dilemmas. Graphical abstract