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.

互惠会被认知错误破坏，错误会导致互动的个体之间对过去的行为产生分歧。赢-留-输-换档和慷慨的以牙还牙等策略可以在感知错误后重新建立合作，但前提是错误很少出现。我们引入了针锋相对的仲裁 (ATFT)，这是一种使用第三方仲裁来调整玩家对当他们不同意时发生的事情的信念的策略。我们表明，当仲裁适度准确时，ATFT 是一个强大的子博弈完美均衡，并且在针对一系列缺陷、合作、忽视仲裁或不必要地调用仲裁的策略时是进化稳定的。当认知错误频繁发生、仲裁成本高昂或仲裁存在偏见时，ATFT 可能会持续存在。