Extortion provides alternative routes to the evolution of cooperation in structured populations

Abstract

In this paper, we study the evolution of cooperation in structured populations (individuals are located on either a regular lattice or a scale-free network) in the context of repeated games by involving three types of strategies, namely, unconditional cooperation, unconditional defection, and extortion. The strategy updating of the players is ruled by the replicator-like dynamics. We find that extortion strategies can act as catalysts to promote the emergence of cooperation in structured populations via different mechanisms. Specifically, on regular lattice, extortioners behave as both a shield, which can enwrap cooperators inside and keep them away from defectors, and a spear, which can defeat those surrounding defectors with the help of the neighboring cooperators. Particularly, the enhancement of cooperation displays a resonance-like behavior, suggesting the existence of optimal extortion strength mostly favoring the evolution of cooperation, which is in good agreement with the predictions from the generalized mean-field approximation theory. On scale-free network, the hubs, who are likely occupied by extortioners or defectors at the very beginning, are then prone to be conquered by cooperators on small-degree nodes as time elapses, thus establishing a bottom-up mechanism for the emergence and maintenance of cooperation.