Evolution of cooperation in multigame with environmental space and delay

Replicator dynamics is widely used in evolutionary game theory, however, most previous studies on replicator dynamics focus on single games and ignore multiple social dilemmas encountered by individuals in a population. This paper uses replicator dynamics to construct a multigame system with environmental space and delay based on three social dilemmas. For the non-delayed and delayed multigame systems, rich dynamics for stability, bistability, transcritical bifurcation, Hopf bifurcation, and the direction, stability and periodic variation of periodic solutions are comprehensively investigated. Accordingly, we use numerical simulations to assist in exploring the effects of multigame, environmental space, and time delay on strategic dynamics. The results show that large proportions of snowdrift game and stag hunt game are conducive to the prosperity of cooperators, and defectors are easy to survive when the proportion of prisoner's dilemma is large. The cooperator gains the advantage of benefit distribution from environmental space, or the defector gets less benefit distribution as punishment, which will make pure cooperation the dominant strategy. Furthermore, environmental space can allow cooperation and defection to coexist oscillatingly. Interestingly, large delays reverse the coexistence of cooperation and defection to a situation dominated by the purely cooperative strategy.