Should drug policy be aimed at cartel leaders? Breaking down a peaceful equilibrium

Experience from the last decade in Colombia and Mexico suggests that violence increases when governments achieve their objective of beheading and fragmenting drug trafficking organizations (DTOs). In this paper I provide a theoretical framework to understand this behavior. Drawing elements from industrial organization, I model DTOs as firms that collude by not attacking each other in order to increase their profits. DTOs always collude when they interact repeatedly; thus, previous analyses focusing on a static Nash equilibrium miss an important part of the dynamics between DTOs. I show that a peaceful equilibrium arises if there are only a few DTOs that care enough about the future. Policies resulting either in a larger number of DTOs or in more impatient leaders increase violence between DTOs without reducing supply. On the other hand, policies that reduce the productivity of DTOs, without directly attacking their leaders and fragmenting them, are more desirable since they can curb supply, although this comes at the cost of increased violence if the elasticity of demand is below a certain threshold. I calculate this threshold, which is a refinement of the value suggested by Becker et al. (2006) for consumer markets.