We have talked about the prisoner’s dilemma in class but what is also of interest is the effect game theory plays in the “game” played between criminals and the police and the result it has on the unsuspecting public. One of the things Ehud Guttel and Barak Medina discuss in their paper is how criminal sanctions can harm the more vulnerable victims as a result of game theory.

In their model the level of sanctions against a criminal determines the volume of his illegal activity. Say there are two neighborhoods, vulnerable (V) and less vulnerable (LV), with the probability of a criminal’s success in performing his crime is in higher in V than LV. Then a criminal would most definitely act in neighborhood LV if there were no police presence. Since police resources are finite, police cannot be in both neighborhoods at the same time and if captured the burglar bears a sanction that could make his net payoff negative. If the criminal operates only in one neighborhood the police increase their presence there as a counter strategy. Therefore the only way to reach Nash equilibrium is if both players use mixed strategies and randomize which neighborhood they act in.

Since the police’s goal is to reduce the volume of crimes, they can try to do so by decreasing activity in LV such that the criminal will act only in LV where he has a lower chance of success in succeeding. However though his success rate is lower in LV, the reduced police presence means that the probability of apprehension is also low and the number of criminal actswill increase and result in a larger number of victims. The sanction against the criminal restricts the expected payoff and therefore the total number of criminal acts but not the distribution of his activity. In contrast police allocation is affected by the severity of the sanction and a move towards harsher sanctions will induce a police move from V to LV. Now neighborhood LV benefits from both the sanction and the police presence in their neighborhood but neighborhood V are harmed for the exact same reasons. The result is that the more vulnerable victims in neighborhood V will have a spike in criminal activity even with the net decrease in crime.

Guttel and Medina specifically use a burglar as an example and assign numerical values for probabilities, payoffs and sanctions. There game theory logic though is discussed in the first seven pages of their paper. I find that their theory provides a unique look into how game theory may be used to produce arguments that at first may seem counterintuitive.

Source: Less Crime, More (Vulnerable) Victims: Game Theory and the Distributional Effects of Criminal Sanctions