Consider a model of crime where a person decides to commit a crim C or not N. Simultaneously, a policeman decides to engage in a high level of enforcement H or low level L. If the person does not commit a crime, they receive a payoff of 0. If they commit a crime they receive a payoff of -1 if caught and 2 if not caught. The policeman will not catch a criminal if they have a low level of enforcement, but they also do not expend any effort, so their payoff is always zero. A policeman exerting a high level of enforcement receives a payoff of 5 if they catch the criminal and -5 if no crime is committed due to the wasted effort. Represent the game in normal form. Solve for all Nash equilibria. Interpret the equilibria: explain in words the economic significance. In particular, comment on the likelihood of whether uncaught crime might occur. Explain why or why not.
Leave a Reply