Oscilliations in the Enforcement of Law: an Evolutionary Analysis

The 2´2 inspection game has been frequently employed to model the problem of law enforcement. This game is notoriously troublesome, because (a) its unique Nash equilibrium is never strict and (b) by playing their maximin strategies players can secure the same payoff they get when both play their Nash equilibrium strategies. According to Holler (1993), this fact might explain why the economic approach to law enforcement is not likely to generate clear-cut predictions. In this paper I employ a standard replicator dynamics model to show that if the inspection game is played by two large populations of players then (a) oscillations in the level of enforcement and law infractions are likely to emerge, and (b) on average the frequency of law infractions equals the Nash equilibrium value, even if we assume that some of the players in both populations use their maximin strategies. The result holds for all payoff positive and payoff monotone dynamics. Some implications for the economic approach to law enforcement are discussed.