Coevolution of multi-game resolves social dilemma in network population

It is an open question to understand the emergence and maintenance of cooperation in nature and society. Aim to this issue, evolutionary game theory in networked population and its various derivations, like mixing game and multi-game, have proved an effective way to resolve the social dilemma. In this work, we propose the coevolution framework of strategy and multi-game: if a player, in prisoner's dilemma game, successively keeps its strategy constant for several times (referred as memory step), it will have opportunity to participate in snow drift game, which has lower dilemma strength than prisoner's dilemma game. Of particular, it is unveiled that for short memory step, the larger the value of sucker's payoff is, the higher frequency of cooperation will be. While for long memory step, middle sucker's payoff provides a best environment for cooperation. For all these findings, we also provide theoretical analysis, which guarantees further validation.