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Dependence of evolutionary cooperation on the additive noise to the enhancement level in the spatial public goods game

Either in societies or economic cycles, the benefits of a group can be affected by various unpredictable factors. We study effects of additive spatiotemporal random variations on the evolution of cooperation by introducing them to the enhancement level of the spatial public goods game. Players are located on the sites of a two-dimensional lattice and gain their payoffs from games with their neighbors by choosing cooperation or defection. We observe that a moderate intensity of variations can best favor cooperation at low enhancement levels, which resembles classical coherence resonance. Whereas for high enhancement levels, we find that the random variations cannot increase the cooperation level, but hamper cooperation instead. This discrepancy is attributed to the different roles the additive variations played in the early and late stages of evolution. In the early stage of evolution, the additive variations increase the survival probability of the players with lower average payoffs. However, in the late stage of evolution, the additive variations can promote defectors to destroy the cooperative clusters that have been formed. Our results indicate that additive spatiotemporal noise may not be as universally beneficial for cooperation as the spatial prisoner's dilemma game.