Playing against the fittest: A simple strategy that promotes the emergence of cooperation

Understanding the emergence and sustainability of cooperation is a fundamental problem in evolutionary biology and is frequently studied by the framework of evolutionary game theory. A very powerful mechanism to promote cooperation is network reciprocity, where the interaction patterns and opportunities for strategy spread of agents are constrained to limited sets of permanent interactions partners. Cooperation survives because it is possible for closeknit communities of cooperation to be shielded from invasion by defectors. Here we show that parameter ranges in which cooperation can survive are strongly expanded if game play on networks is skewed towards more frequent interactions with more successful neighbours. In particular, if agents exclusively select neighbors for game play that are more successful than themselves, cooperation can even dominate in situations in which it would die out if interaction neighbours were chosen without a bias or with a preference for less successful opponents. We demonstrate that the “selecting fitter neighbours” strategy is evolutionarily stable. Moreover, it will emerge as the dominant strategy out of an initially random population of agents. Introduction. – A variety of socialand non-social organisms display altruism [11]. Altruism describes the ability to cooperate for joint benefit even at a cost to the individual. This scenario has frequently been studied by the prisoner’s dilemma [12], in which two individuals simultaneously make a decision to cooperate (C) or defect (D). Cooperation gives a benefit b to the recipient, but comes at a cost c to the donor. Introducing the costbenefit ratio r = c/(b − c) and normalizing, a frequently used parametrization of the game is that mutual cooperation is rewarded by R = 1 for both players. A cooperator interacting with a defector receives S = −r while the defector obtains a payoff T = 1 + r. Mutual defection results in the same payoff P = 0 for both opponents. For 0 < r < 1 payoffs are ranked T > R > P > S and 2R > T + S, such that for one player independent of the other player’s strategy, defection always results in a better outcome. The inferiority of the payoff for one-sided or mutual defection to mutual cooperation constitutes the dilemma setting. The evolution of cooperation is conveniently studied in the framework of evolutionary game theory [2]. One considers a population of agents whose strategies spread in the population according to their success in game play. Because defectors always earn larger payoffs than cooperators, cooperation cannot survive in well-mixed situations in which agents can interact with all other agents in the population. In this case defection is the evolutionarily stable strategy. As shown by studies of evolutionary games in space [3,4,6] and more recently on other types of complex networks [5, 7–10, 16, 17] the dominance of defection can be reduced if interaction patterns are restricted to a finite set of permanent opponents. Limited interaction patterns are conveniently described by spatial grids or complex networks such as scale-free or small-world networks [13, 14]. On a network, agents interact in playing the prisoner’s dilemma game with their network neighbours. Strategy evolution is described by a process whereby agents can adopt the strategies of better performing neighbours. In such a setting cooperators can form tightly-knit clusters of cooperation that are shielded from the invasion of defectors. Nevertheless, even though cooperation is boosted by