Graduated Punishments in Public Good Games

I explain the ubiquitous use of graduated punishments by studying a repeated public good game in which a social planner imperfectly monitors agents to detect shirkers. Agents' cost of contributing is private information and administering punishments is costly. Using graduated punishments can be optimal for two reasons. It increases the price of future wrongdoing (temporal spillover effect) and it can lead to bad types revealing themselves (screening effect). The temporal spillover effect is always present if graduated punishments prevail, but screening need not occur if agents face a finite horizon. Whether or not a screening effect is exploited has a substantial impact on both outcomes and actual punishments. If the temporal spillover effect is sufficiently strong, then first-time shirkers are merely warned.