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An active participation of players in evolutionary games depends on severalfactors, ranging from personal stakes to the properties of the interactionnetwork. Diverse activity patterns thus have to be taken into account whenstudying the evolution of cooperation in social dilemmas. Here we study theweak prisoner's dilemma game, where the activity of each player is determinedin a probabilistic manner either by its degree or by its payoff. Whiledegree-correlated activity introduces cascading failures of cooperation thatare particularly severe on scale-free networks with frequently inactive hubs,payoff-correlated activity provides a more nuanced activity profile, whichultimately hinders systemic breakdowns of cooperation. To determine optimalconditions for the evolution of cooperation, we introduce an exponential decayto payoff-correlated activity that determines how fast the activity of a playerreturns to its default state. We show that there exists an intermediate decayrate, at which the resolution of the social dilemma is optimal. This can beexplained by the emerging activity patterns of players, where the inactivity ofhubs is compensated effectively by the increased activity of average-degreeplayers, who through their collective influence in the network sustain a higherlevel of cooperation. The sudden drops in the fraction of cooperators observedwith degree-correlated activity therefore vanish, and so does the need for thelengthy spatiotemporal reorganization of compact cooperative clusters. Theabsence of such asymmetric dynamic instabilities thus leads to an optimalresolution of social dilemmas, especially when the conditions for the evolutionof cooperation are strongly adverse.

From degree-correlated to payoff-correlated activity for an optimal resolution of social dilemmas