Punishment is a potential mechanism to stabilise cooperation between self-regarding agents. Theoretical and empirical studies on the importance of a punitive reputation have yielded conflicting results. Here, we propose that a variety of factors interact to explain why a punitive reputation is sometimes beneficial and sometimes harmful. We predict that benefits are most likely to occur in forced play scenarios and in situations where punishment is the only means to convey an individual's cooperative intent and willingness to uphold fairness norms. By contrast, if partner choice is possible and an individual's cooperative intent can be inferred directly, then individuals with a nonpunishing cooperative reputation should typically be preferred over punishing cooperators.
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