Many legal systems are designed to punish repeat offenders more severely than first time offenders.However, existing economic literature generally offers either mixed or qualified results regarding optimal punishment of repeat offenders. This paper analyzes optimal punishment schemes in a two period model, where the social planner announces possibly-different sanctions for offenders based on their detection history. When offenders learn how to evade the detection mechanism employed by the government, escalating punishments can be optimal. The contributions of this paper can be listed as follows: First, it identifies and formalizes a source which may produce a marginal effect in the direction of punishing repeat offenders more severely, namely learning. Next, it identifies conditions under which the tendency in legal systems to punish repeat offenders more severely is justified. Overall, the findings suggest that the traditional variables identified so far in the literature are not the only relevant ones in deciding how repeat offenders should be punished, and that learning dynamics should also be taken into account.

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In the law enforcement literature there is a presumption-supported by some experimental and econometric evidence-that criminals are more responsive to increases in the certainty than the severity of punishment. Under a general set of assumptions, this implies that criminals are risk seeking. We show that this implication is no longer valid when forfeiture of illegal gains and the possibility of unsuccessful attempts are considered. Therefore, when drawing inferences concerning offenders' attitudes toward risk based on their responses to various punishment schemes, special attention must be paid to whether and to what extent offenders' illegal gains can be forfeited and whether increases in the probability of punishment affect the probability of attempts being successful. We discuss policy implications related to our observations.

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