Double resonance in cooperation induced by noise and network variation for an evolutionary prisoner's dilemma

We study effects of slowly varying small-world topology and additive spatiotemporal random variations, introduced to the payoffs of a spatial prisoner's dilemma game, on the evolution of cooperation. We show that there exists an optimal fraction of shortcut links, constituting the variable complex network of participating players of the game, for which noise-induced cooperation is resonantly enhanced, thus marking a double resonance phenomenon in the studied system. The double resonance is attributed to the time-dependence of the connectivity structure that induces a tendency towards the mean-field behaviour in the limit of random graphs. We argue that random payoff disturbances and complex network topology are two potent extrinsic factors able to boost cooperation, thus representing a viable escape hatch out of evolutionary stalemate.