Indirect reciprocity can stabilize cooperation without the second-order free rider problem

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Abstract
Models of large-scale human cooperation take two forms. ‘Indirect reciprocity’1 occurs when individuals help others in order to uphold a reputation and so be included in future cooperation. In ‘collective action’2, individuals engage in costly behaviour that benefits the group as a whole. Although the evolution of indirect reciprocity is theoretically plausible3,4,5,6, there is no consensus about how collective action evolves. Evidence suggests that punishing free riders can maintain cooperation7,8,9, but why individuals should engage in costly punishment is unclear. Solutions to this ‘second-order free rider problem’ include meta-punishment10, mutation11, conformism12, signalling13,14,15 and group-selection16,17,18. The threat of exclusion from indirect reciprocity can sustain collective action in the laboratory19. Here, we show that such exclusion is evolutionarily stable, providing an incentive to engage in costly cooperation, while avoiding the second-order free rider problem because punishers can withhold help from free riders without damaging their reputations. However, we also show that such a strategy cannot invade a population in which indirect reciprocity is not linked to collective action, thus leaving unexplained how collective action arises.

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