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

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 plausible^3,4,5,6, there is no consensus about how collective action evolves. Evidence suggests that punishing free riders can maintain cooperation^7,8,9, but why individuals should engage in costly punishment is unclear. Solutions to this ‘second-order free rider problem’ include meta-punishment¹⁰, mutation¹¹, conformism¹², signalling^13,14,15 and group-selection^16,17,18. 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.