  Cooperation in human society is sustained by reputation. In general, the
reputation of an individual is determined by others who observe his behavior,
but this rarely happens in private situations. This may cause people to behave
inconsistently, cooperating in public and not cooperating in private. A
previous experiment showed that people gave a lower reputation to an individual
who cooperated in public but defected in private rather than a consistently
uncooperative individual regardless of public and private situations. However,
the reason behind this is unclear. Here, we study how cooperation and the
reputational mechanism co-evolve on the condition that two types of interaction
(public and private) exist. The simulation results show that the evolved social
norm is characterized by at least one of the following: preference for
consistent or aversion of inconsistent behavior in both interactions when the
risk that behaviors in private interactions are observed exceeds a certain
threshold. We also find that such social norms promote cooperation in private
situations as well as in public ones.
