The evolution of moral rules in a model of indirect reciprocity with private assessment

Moral rules allow humans to cooperate by indirect reciprocity. Yet,
it is not clear which moral rules best implement indirect reciprocity and
are favoured by natural selection. Previous studies either considered only
public assessment, where individuals are deemed good or bad by all others, or compared a subset of possible strategies. Here we  ll this gap by
identifying which rules are evolutionary stable strategies (ESS) among all
possible moral rules while considering private assessment. We develop
an analytical model describing the frequency of long-term cooperation,
determining when a strategy can be invaded by another. We show that
there are numerous ESSs in absence of errors, which however cease to
exist when errors are present. We identify the underlying properties of
cooperative ESSs. Overall, this paper provides a  rst exhaustive evolutionary invasion analysis of moral rules considering private assessment.
Moreover, this model is extendable to incorporate higher-order rules and
other processes.