Reciprocity is undermined by perception errors, mistakes that cause disagreement between interacting individuals about past behaviour. Strategies such as win–stay–lose–shift and generous tit-for-tat can re-establish cooperation following a perception error, but only when errors arise infrequently. We introduce arbitration tit-for-tat (ATFT), a strategy that uses third-party arbitration to align players’ beliefs about what transpired when they disagree. We show that, when arbitration is moderately accurate, ATFT is a strong subgame-perfect equilibrium and is evolutionarily stable against a range of strategies that defect, cooperate, ignore arbitration or invoke arbitration unnecessarily. ATFT can persist when perception errors are frequent, arbitration is costly or arbitration is biased. The need for third parties to resolve perception errors could explain why reciprocity is rare in other animals despite opportunities for repeated interactions and why human reciprocity is embedded within culturally transmitted moral norms in which community monitoring plays a role.
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There is no empirical data associated with this paper.
Mathematica and Matlab scripts used to solve the fitness equations, perform Monte Carlo simulations and create the plots are publicly available at https://osf.io/weu4b/?view_only=7fb48e283424447c930d0455aaa36912.
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We thank M. Hoffman for help with proving that ATFT is subgame perfect. We also thank J. Silk, P. Richerson and J. Henrich for useful comments. This research was funded by the John Templeton Foundation (grant no. 48952). The views expressed in this publication are those of the authors and do not necessarily reflect the views of the funding agency.
The authors declare no competing interests.
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Boyd, R., Mathew, S. Arbitration supports reciprocity when there are frequent perception errors. Nat Hum Behav 5, 596–603 (2021). https://doi.org/10.1038/s41562-020-01008-1