Who's Who in Crime Network. Wanted the Key Player

Criminals are embedded in a network of relationships. Social ties among criminals are modeled by means of a graph where criminals compete for a booty and benefit from local interactions with their neighbours. Each criminal decides in a non-cooperative way how much crime effort he will exert. We show that the Nash equilibrium crime effort of each individual is proportional to his equilibrium Bonacich-centrality in the network, thus establishing a bridge to the sociology literature on social networks. We then analyze a policy that consists of finding and getting rid of the key player, that is, the criminal who, once removed, leads to the maximum reduction in aggregate crime. We provide a geometric characterization of the key player identified with an optimal inter-centrality measure, which takes into account both a player's centrality and his contribution to the centrality of the others. We also provide a geometric characterization of the key group, which generalizes the key player for a group of criminals of a given size. We finally endogeneize the crime participation decision, resulting in a key player policy, which effectiveness depends on the outside opportunities available to criminals.