A Note on the Optimal Punishment for Repeat Offenders

Agents may commit a crime twice. The act is inefficient so that the agents are to be deterred. The agents are wealth constrained so that increasing the fine for the first offense means a reduction in the sanction for the second offense and vice versa. The agents may follow history dependent strategies. The government seeks to minimize the probability of apprehension. The optimal sanction scheme is decreasing rather than increasing in the number of offenses. Indeed, the sanction for the first offense equals the entire wealth while the sanction for the second offense is zero.