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A Dynamic Analysis of Criminal Networks

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Abstract
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

Suggested Citation

  • Luca Colombo & Paola Labrecciosa & Agnieszka Rusinowska, 2022. "A Dynamic Analysis of Criminal Networks," Documents de travail du Centre d'Economie de la Sorbonne 22006, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:22006
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    More about this item

    Keywords

    differential games; Markov Perfect Equilibrium; social networks; criminal networks; Bonacich centrality;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • K42 - Law and Economics - - Legal Procedure, the Legal System, and Illegal Behavior - - - Illegal Behavior and the Enforcement of Law

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