Cooperation in changing environments: Irreversibility in the transition to cooperation in networks

TL;DR

This paper studies how cooperation levels in networked Prisoner's Dilemma games can exhibit hysteresis, with cooperation persisting or reversing depending on the parameter changes and network structure.

Contribution

It demonstrates the existence of cooperation hysteresis cycles in complex networks and explains the underlying mechanisms involving cooperator clusters and strategic fixation.

Findings

Hysteresis cycles occur in cooperation levels on networks.

Reversibility depends on reaching critical parameter thresholds.

Cooperator clusters influence lagging behavior.

Abstract

In the framework of the evolutionary dynamics of the Prisoner's Dilemma game on complex networks, we investigate the possibility that the average level of cooperation shows hysteresis under quasi-static variations of a model parameter (the "temptation to defect"). Under the "discrete replicator" strategy updating rule, for both Erdos-Renyi and Barabasi-Albert graphs we observe cooperation hysteresis cycles provided one reaches tipping point values of the parameter; otherwise, perfect reversibility is obtained. The selective fixation of cooperation at certain nodes and its organization in cooperator clusters, that are surrounded by fluctuating strategists, allows the rationalization of the "lagging behind" behavior observed.