Many institutional arrangements suggest that punishments and rewards each play a separate role in providing incentives. In New York City’s recent negotiations with its teacher’s union, for instance, the city sought a contract that would strengthen school principals’ ability to assign teachers to be cafeteria monitors, in part because this allows them to punish underperforming teachers. The cont...

Case studies of self-enforcing cooperation in repeated interactions usually find that the punishments inflicted on deviators are mild to start with, and increase only if there is evidence of persistent deviation. We model this using a combination of imperfect monitoring and asymmetric information in a one-sided prisoner’s dilemma. Call the player with the temptation to cheat player B, and the o...