title: From degree-correlated to payoff-correlated activity for an optimal resolution of social dilemmas.
abstract: 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.
authors.affiliation: Institute for Biocomputation and Physics of Complex Systems, University of Zaragoza, Zaragoza E-50018, Spain.
authors.forename: Alberto
authors.initials: A
authors.lastname: Aleta
authors.affiliation: Institute for Biocomputation and Physics of Complex Systems, University of Zaragoza, Zaragoza E-50018, Spain.|Department of Theoretical Physics, University of Zaragoza, Zaragoza E-50009, Spain.
authors.forename: Sandro
authors.initials: S
authors.lastname: Meloni
authors.affiliation: Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, Maribor SI-2000, Slovenia.|CAMTP - Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, Maribor SI-2000, Slovenia.
authors.forename: Matjaž
authors.initials: M
authors.lastname: Perc
authors.affiliation: Institute for Biocomputation and Physics of Complex Systems, University of Zaragoza, Zaragoza E-50018, Spain.|Department of Theoretical Physics, University of Zaragoza, Zaragoza E-50009, Spain.|Complex Networks and Systems Lagrange Lab, Institute for Scientific Interchange, Turin 10126, Italy.
authors.forename: Yamir
authors.initials: Y
authors.lastname: Moreno
mesh_terms: D003299:Cooperative Behavior; D005716:Game Theory; D006801:Humans; D007398:Interpersonal Relations; D008954:Models, Biological