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Advantageous punishers in nature

The evolution and maintenance of cooperation fascinated researchers for several decades. Recently, theoretical models and experimental evidence show that costly punishment may facilitate cooperation in human societies, but may not be used by winners. The puzzle how the costly punishment behaviour evolves can be solved under voluntary participation. Could the punishers emerge if participation is compulsory? Is the punishment inevitably a selfish behaviour or an altruistic behaviour? The motivations behind punishment are still an enigma. Based on public goods interactions, we present a model in which just a certain portion of the public good is divided equally among all members. The other portion is distributed to contributors when paying a second cost. Contributors who are willing to pay a second cost can be costly (and then altruistic) punishers, but they can also flourish or dominate the population, in this case we may call them "advantageous punishers". We argue that most of successful cooperators and punishers in nature are advantageous punishers, and costly punishment mostly happens in humans. This indicates a universal surviving rule: contributing more and gaining more. Our models show theoretically that the original motivation behind punishment is to retrieve deserved payoff from their own contributions, a selfish incentive.