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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 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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Figure 1: Evolutionary dynamics of the Shunner, Defector and Cooperator strategies, plotted in trilinear coordinates.
Figure 2: The threshold degree of assortment (r*, derived in the Supplementary Information) necessary for rare Shunners to invade as a function of the number of mutual aid periods, 1/(1 - w), for two different collective action benefit cost ratios, B/C.
Figure 3: The threshold frequency at which Shunners increase (p*) as a function of the number of mutual aid periods, 1/(1 - w), for different levels of assortment, r.

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Acknowledgements

We thank C. Barrett, S. Bowles, E. Fehr, H. Gintis, J. Henrich, R. Kurzban, S. Naficy, C. Navarrete, D. Penn, J. Silk and the Experimental Biological Anthropology Group for discussions. We especially thank K. Haley for developing the ideas presented in this paper. K.P. was funded by an NSF Graduate Research Fellowship.

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Correspondence to Karthik Panchanathan.

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Supplementary information

Supplementary Equations

This section provides complete, analytical derivations of the models presented in the main text. This section is broken down into three subsections, representing the three different strategy mixes analysed. (DOC 435 kb)

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Panchanathan, K., Boyd, R. Indirect reciprocity can stabilize cooperation without the second-order free rider problem. Nature 432, 499–502 (2004). https://doi.org/10.1038/nature02978

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