TO COMMIT OR NOT TO COMMIT A CRIME. A CRIMINAL NETWORK MODEL AND AN ALGORITHM FOR ITS ANALYSIS

Abstract

Here we introduce and investigate a mathematical model of delinquent networks. This problem is formulated in the framework of game theory, one of whose main concepts is the Nash equilibrium. We discuss how the problem of finding a Nash equilibrium leads to a constraint satisfaction problem, and how it can be analyzed using methods of statistical mechanics whose mathematical formalization is a very active research topic today. From the computational point of view, such methods give rise to algorithms of passage of messages that allow to obtain statistical properties of interest, such as the level of average delinquency activity and the number of Nash equilibria.

Keywords

• Sistemas complejos
• teoría de juegos
• modelado computacional
• modelos en redes
• teoría de probabilidad
• redes delincuenciales
• mecánica estadística.