Temporal networks provide a unifying understanding of the evolution of cooperation

TL;DR

This paper demonstrates that temporal heterogeneity in networks enhances the likelihood of cooperation fixation, unifying previous findings across equilibrium and non-equilibrium frameworks.

Contribution

It provides the first comprehensive analysis showing that temporal degree heterogeneity promotes cooperation in both theoretical and empirical networks, resolving previous conflicting results.

Findings

Temporal heterogeneity increases cooperation fixation probability.

Contrary to static networks, temporal heterogeneity promotes cooperation.

Unified understanding across equilibrium and non-equilibrium frameworks.

Abstract

Understanding the evolution of cooperation in structured populations represented by networks is a problem of long research interest, and a most fundamental and widespread property of social networks related to cooperation phenomena is that the node's degree (i.e., number of edges connected to the node) is heterogeneously distributed. Previous results indicate that static heterogeneous (i.e., degree-heterogeneous) networks promote cooperation in stationarity compared to static regular (i.e., degree-homogeneous) networks if equilibrium dynamics starting from many cooperators and defectors is employed. However, the above conclusion reverses if we employ non-equilibrium stochastic processes to measure the fixation probability for cooperation, i.e., the probability that a single cooperator successfully invades a population. Here we resolve this conundrum by analyzing the fixation of cooperation on temporal (i.e., time-varying) networks. We theoretically prove and numerically confirm that on both synthetic and empirical networks, contrary to the case of static networks, temporal heterogeneous networks can promote cooperation more than temporal regular networks in terms of the fixation probability of cooperation. Given that the same conclusion is known for the equilibrium fraction of cooperators on temporal networks, the present results provide a unified understanding of the effect of temporal degree heterogeneity on promoting cooperation across two main analytical frameworks, i.e., equilibrium and non-equilibrium ones.