The evolution of cooperation affected by aspiration-driven updating rule in multi-games with voluntary participation

Abstract We have demonstrated multi-games with voluntary participation can promote cooperation and found aspiration-driven updating rule can also facilitate cooperation to some degree. Stimulated by these, we combine the two mechanisms and investigate the evolution of cooperation. In our work, the population is randomly divided into two types, one type players play the PDG, while the other type players play SG. At the same time, a part of players randomly select to use the aspiration-driven updating rule, and the other part of players choose to use the Fermi-function based strategy adoption rule. Besides, players have three strategies - cooperation, defection and going it alone- to choose. We reveal that both the diversity of sucker's payoff and updating strategy can facilitate cooperation to some degree. Moreover, larger magnitude of sucker's payoff and less players using the aspiration-driven rule can improve cooperation resulting from spatial distribution of strategies. And players playing SG play a more important role to enhance cooperation than players playing PDG, which is due to the special network reciprocity. Furthermore, the easily satisfied players intend to cooperate, while the greedy players intend to be loners to avoid obtaining nothing.