  An active participation of players in evolutionary games depends on several
factors, ranging from personal stakes to the properties of the interaction
network. Diverse activity patterns thus have to be taken into account when
studying the evolution of cooperation in social dilemmas. Here we study the
weak prisoner's dilemma game, where the activity of each player is determined
in a probabilistic manner either by its degree or by its payoff. While
degree-correlated activity introduces cascading failures of cooperation that
are particularly severe on scale-free networks with frequently inactive hubs,
payoff-correlated activity provides a more nuanced activity profile, which
ultimately hinders systemic breakdowns of cooperation. To determine optimal
conditions for the evolution of cooperation, we introduce an exponential decay
to payoff-correlated activity that determines how fast the activity of a player
returns to its default state. We show that there exists an intermediate decay
rate, at which the resolution of the social dilemma is optimal. This can be
explained by the emerging activity patterns of players, where the inactivity of
hubs is compensated effectively by the increased activity of average-degree
players, who through their collective influence in the network sustain a higher
level of cooperation. The sudden drops in the fraction of cooperators observed
with degree-correlated activity therefore vanish, and so does the need for the
lengthy spatiotemporal reorganization of compact cooperative clusters. The
absence of such asymmetric dynamic instabilities thus leads to an optimal
resolution of social dilemmas, especially when the conditions for the evolution
of cooperation are strongly adverse.
