Violence and law enforcement in markets for illegal goods

In this article, I try to establish optimal law enforcement efforts in markets for illegal goods taking into account both consumption and violence externalities. I model competition between firms as a Cournot duopoly game where they produce an illegal good and sabotage each other to gain a larger share of the market. I show that socially optimal law enforcement can result in any of the following corner solutions: letting firms produce freely, partially intervene punishing one firm more than the other, or fully intervene to eliminate them both. Which solution is optimal depends on the size of consumption and violence externalities; the direct costs of law enforcement and sabotage; the weight of profits in the welfare function of the authority; and how cautious is the authority avoiding violence externalities while enforcing the law.