Optimal control of cartel violence: Multiple equilibria, narrow corridors, and weak Skiba curves

Abstract

We present an optimal control model for evaluating how Mexico might best use two instruments (security measures and social programs) to control a pair of criminal cartels that are in lethal conflict with each other. For our model and parameters being made as realistic as possible, our analysis is meant to provide guidance to the Mexican government. In this presentation we will mostly focus on variations on our model and parameters that reveal interesting structural features, because we believe that the basic architecture of our model is intrinsically interesting to the optimal control community - both with respect to the structure of the solutions and their economic interpretation. Our results are derived with the help of bifurcation analyses and include solutions with as many as ten equilibria, some separated by double and even triple Skiba points.