A dynamic analysis of criminal networks
基于微分博弈将静态犯罪网络模型扩展为动态，发现均衡犯罪率与中心度不再成比例，且动态中的关键罪犯可能随时间变化，对执法策略有启示。
We take a novel approach based on differential games to the study of criminal networks. We extend the static crime network game (Ballester et al., 2006, 2010) to a dynamic setting where criminal activities negatively impact the accumulation of total wealth in the economy. We derive a Markov Feedback Equilibrium and show that, unlike in the static crime network game, the vector of equilibrium crime rates is not necessarily proportional to the vector of Bonacich centralities. Next, we conduct a comparative dynamic analysis with respect to the network size, the network density, and the marginal expected punishment, finding results in contrast with those arising in the static crime network game. We also shed light on a novel issue in the network theory literature, i.e., the existence of a voracity effect . Finally, we study the problem of identifying the optimal target in the population of criminals when the planner's objective is to minimize aggregate crime at each point in time. Our analysis shows that the key player in the dynamic and the static setting may differ, and that the key player in the dynamic setting may change over time.