A Dynamic Analysis of Criminal Networks

The paper presents a novel approach based on differential games to the study of criminal networks. We extend the static crime network game (Ballester et al., 2004, 2006) to a dynamic setting. First, we determine the relationship between the Markov Perfect Equilibrium (MPE) and the vector of Bonacich centralities. The established proportionality between the Nash equilibrium and the Bonacich centrality in the static game does not hold in general in the dynamic setting. Next, focusing on regular networks, we provide an explicit characterization of equilibrium strategies, and conduct comparative dynamic analysis with respect to the network size, network density, and implicit growth rate of total wealth in the economy. Contrary to the static game, where aggregate equilibrium increases with network size and density, in the dynamic setting, more criminals or more connected criminals can lead to a decrease in total crime, both in the short run and at the steady state. We also examine another novel issue in the network theory literature, i.e., the existence of a voracity effect, occuring when an increase in the implicit growth rate of total wealth in the economy lowers economic growth. We do identify the presence of such a voracity effect in our setting