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First I show that for wealth-constrained agents who may commit an act twice the optimal sanctions are the offender's entire wealth for the first and zero for the second crime. Then I ask the question whether this decreasing sanction scheme is subgame perfect (time consistent), that is, does a rent-seeking government stick to this sanction scheme after the first crime has occurred. If the benefit and/or the harm from the crime are not too large, this is indeed the case; otherwise, equal sanctions for both crimes are optimal. (JEL D82, K47, K42)
I. INTRODUCTION
The literature on optimal law enforcement typically assumes that the government can commit to sanction schemes.' This means the government can use any set of threats to penalize wrongdoers. In particular, if a crime occurs, the government actually sanctions the wrongdoers even though, ex post, it may have no incentive to do so. Potential wrongdoers believe that the government will carry out the threat at any cost and, therefore, do not engage in the act in the first place.
In this article I give up the assumption that the government can commit to whatever sanction scheme. I consider the analysis of optimal sanctions without the possibility to commit important because judges often have a lot of discretion as to the size of the penalty; they may, for example, adjust sanctions to the financial possibilities, age, education, and so on of the wrongdoer. Accordingly, I allow only for sanctions that the government actually wishes to implement should a crime have occurred.
Ruling out full commitment changes the optimal enforcement schemes. Suppose, for example, the government does not care about the sanction, as is typically assumed in the literature. Then it will not enforce the penalty if a crime has happened given that there is, say, a small cost of doing so. The rational criminal will anticipate the ex post enforcement behavior of the government. Therefore, she will commit the crime because the threat of being sanctioned is not credible. Once one drops the commitment assumption, the typical deterrence equilibria of the law enforcement literature between potential wrongdoers and the government are based on empty threats. In the language of game theory, the equilibria are not subgame perfect or time consistent.
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