Multiple Activities for Socially-Connected Criminals

We consider a network model where individuals exert efforts in two types of activities that are interdependent. These activities can be either substitutes or complements. We focus on criminals that either exert efforts in crime and education (substitutable activities) or crime and drug consumption (complementary activities). We provide a full characterization of the Nash equilibrium of this game for any network structure and show under which condition it exists and is unique. We then derive some comparative statics results that offer strong empirical predictions on the effect of own productivity on both efforts and how network density affects equilibrium outcomes. Finally, we re-examine the key-player policy that consists in determining the criminal who, once removed, reduces total crime the most. We show that, if the planner ignores the fact that criminals have multiple activities, then she can wrongly determine who the key player is.