Diversity of timescale promotes the maintenance of extortioners in a spatial prisoner's dilemma game

Recently, a class of interesting strategies, named extortion strategies, has attracted considerable attention since such extortion strategies can dominate any opponent in a repeated prisoner's dilemma game. In this paper, we investigate the influence of the strategy-selection timescale on the evolution of extortion and cooperation in networked systems. Through connecting the lifetime of individuals' strategies with their fitness, we find that extortioners can form long-term stable relationships with cooperative neighbors, whereas the lifetime of a defection strategy is short according to the myopic best response rule. With the separation of interaction and strategy-updating timescales, the extortioners in a square lattice are able to form stable, cross-like structures with cooperators due to the snowdrift-like relation. In scale-free networks the hubs are most likely occupied by extortioners, who furthermore induce their low-degree neighbors to behave as cooperators. Since extortioners in scale-free networks can meet more cooperators than their counterparts in the square lattice, the latter results in higher average fitness of the whole population than the former. The extortioners play the role of a catalyst for the evolution of cooperation, and the diversity of strategy-selection timescale furthermore promotes the maintenance of extortioners with cooperators in networked systems.