The effect of perceptions competition and learning costs on cooperation in spatial evolutionary multigames

It is a great challenge to correctly understand the evolution and incentives of cooperation. In recent years, the spatial evolutionary multigames have attracted extensive attention from researchers. Actually, for players, not only themselves but also their neighbors will affect their perceptions, which has not been considered in previous works. In addition, changing perceptions has a learning process, which will cause some costs. Inspired by the above facts, we explore the impact of perceptions competition mechanisms and learning costs on the evolution of cooperation in the multigames dilemma, which consists of prisoner game and snowdrift game. Especially, we further explore how different groups can coexist in such a setting. It is found that the heterogeneity of payoffs contributes to network reciprocity and can maintain cooperative behaviors even under unfavorable conditions. Compared with the static multigames mechanism, our perceptions competition mechanism has a higher proportion of cooperators under the same temptation value b and sucker payoff θ, and the cooperators can survive within a larger range of parameters. At the same time, a small cost can effectively maintain a high proportion of cooperators, while an appropriate cost will keep players at a high level of both the proportion of cooperators and the coexistence range. The continuous increase of costs will make our evolutionary mechanism ineffective and turn to static multigames. We also find that the introduction of costs will help different types of players coexist, and with the increase of costs, the coexistence area will first decrease and then increase. Moreover, our main findings are equally applicable to complex networks such as BA networks and random networks.