Fig 1. An action rule specifies how a donor behaves in ‘public’ and ‘private’ interactions with recipients who have either a ‘good’ or ‘bad’ reputation.

The donor’s choice is binary: cooperate or defect. There are 16 different action rules. A social norm describes how (potential) observers evaluate an interaction. The donor’s reputation is updated dependent on the type of interaction (public or private), the recipient’s reputation (good or bad) and the donor’s action (cooperate or defect). There are 256 such second-order social norms.