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We study an evolutionary prisoner's dilemma game with two layered graphs,where the lower layer is the physical infrastructure on which the interactionsare taking place and the upper layer represents the connections for thestrategy adoption (learning) mechanism. This system is investigated by means ofMonte Carlo simulations and an extended pair-approximation method. We considerthe average density of cooperators in the stationary state for a fixedinteraction graph, while varying the number of edges in the learning graph.According to the Monte Carlo simulations, the cooperation is modifiedsubstantially in a way resembling a coherence-resonance-like behavior when thenumber of learning edges is increased. This behavior is reproduced by theanalytical results.

Cooperation enhanced by the difference between interaction and learning neighborhoods for evolutionary spatial prisoner's dilemma games