Abstract
Holding on to one's strategy is natural and common if the later warrants success and satisfaction. This goes against widespread simulation practices of evolutionary games, where players frequently consider changing their strategy even though their payoffs may be marginally different than those of the other players. Inspired by this observation, we introduce an aspiration-based win-stay-lose-learn strategy updating rule into the spatial prisoner's dilemma game. The rule is simple and intuitive, foreseeing strategy changes only by dissatisfied players, who then attempt to adopt the strategy of one of their nearest neighbors, while the strategies of satisfied players are not subject to change. We find that the proposed win-stay-lose-learn rule promotes the evolution of cooperation, and it does so very robustly and independently of the initial conditions. In fact, we show that even a minute initial fraction of cooperators may be sufficient to eventually secure a highly cooperative final state. In addition to extensive simulation results that support our conclusions, we also present results obtained by means of the pair approximation of the studied game. Our findings continue the success story of related win-stay strategy updating rules, and by doing so reveal new ways of resolving the prisoner's dilemma.
Highlights
Evolutionary game theory provides a powerful mathematical framework for studying the emergence and stability of cooperation in social, economic and biological systems [1,2,3,4,5]
Since TwRwPwS, there is an innate tension between individual interests and social welfare that may result in the ‘‘tragedy of the commons’’ [7]
We have tested the impact of different initial configurations, in particular such where cooperators initially have an inherent disadvantage over defectors, and we have discovered that the studied win-stay-lose-learn rule ensures that cooperators are able to spread even from very small numbers
Summary
Evolutionary game theory provides a powerful mathematical framework for studying the emergence and stability of cooperation in social, economic and biological systems [1,2,3,4,5]. The prisoner’s dilemma game, in particular, is frequently considered as a paradigm for studying the emergence of cooperation among selfish and unrelated individuals [6]. The outcome of the prisoner’s dilemma game is governed by pairwise interactions, such that at any instance of the game two individuals, who can either cooperate or defect, play the game against each other by selecting their strategy simultaneously and without knowing what the other player has chosen. Both players receive the reward R upon mutual cooperation, but the punishment P upon mutual defection. Five prominent rules for the successful evolution of cooperation, which may help avert an impeding social decline, are kin selection, direct and indirect reciprocity, network reciprocity as well as group selection, as comprehensively reviewed in [8]
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