Physica A ( ) – Contents lists available at SciVerse ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Crime and punishment: Does it pay to punish? J.R. Iglesias a,b,c,∗ , V. Semeshenko d , E.M. Schneider a , M.B. Gordon e a Instituto de Física, UFRGS, Caixa Postal 15051, 91501-970 Porto Alegre, RS, Brazil b Instituto Nacional de Ciência e Tecnologia de Sistemas Complexos, Caixa Postal 15051, 91501-970 Porto Alegre, RS, Brazil c Programa de Pós-Graduação em Economia, UFRGS, Av. João Pessoa 52, 90040-000 Porto Alegre, RS, Brazil d Academia Nacional de Ciencias Económicas, Av. Alvear 1790, 1014, Buenos Aires, Argentina e Laboratoire LIG/AMA (UMR 5217), University of Grenoble, Centre Equation 4, BP 53, F-38041 Grenoble Cedex 9, France article info Article history: Received 7 April 2011 Received in revised form 22 February 2012 Available online xxxx Keywords: Social systems Sociophysics Crime and punishment Becker’s theory Inequality abstract Crime is the result of a rational distinctive balance between the benefits and costs of an illegal act. This idea was proposed by Becker more than forty years ago (Becker (1968) [1]). In this paper, we simulate a simple artificial society, in which agents earn fixed wages and can augment (or lose) wealth as a result of a successful (or not) act of crime. The probability of apprehension depends on the gravity of the crime, and the punishment takes the form of imprisonment and fines. We study the costs of the law enforcement system required for keeping crime within acceptable limits, and compare it with the harm produced by crime. A sharp phase transition is observed as a function of the probability of punishment, and this transition exhibits a clear hysteresis effect, suggesting that the cost of reversing a deteriorated situation might be much higher than that of maintaining a relatively low level of delinquency. Besides, we analyze economic consequences that arise from crimes under different scenarios of criminal activity and probabilities of apprehension. © 2012 Elsevier B.V. All rights reserved. 1. Introduction Most of the books and movies referring to criminality discuss the offenders point of view: Is crime rewarding? If one sets aside the ethic problem, as discussed by Dostoyevsky in ‘‘Crime and Punishment’’ one can say that crime is rewarding if you are not caught. However, the problem here is not if crime is rewarding but instead if punishment is rewarding or, in other words, if the expenses with police, lawyers, judges, prisons, prison guards, etc., compensate the wealth rubbed off by crime. This is the point discussed by Becker [1] in 1968. But let us first define what kind of crimes are we talking about and what is the retribution for those crimes. One of the widely accepted definitions states that committing a crime is breaking one or more rules or laws, defined by a social group through some kind of social contract. All along history, human societies try to cope with crime either by prevention or punishment. However, these approaches are not independent. Prevention relies on some common moral or religious standards, and in part on the fear of a penalty. Even religion, which provides a moral guide for individuals and societies, makes use of a reward (paradise) and a punishment (hell). In some societies rewards for not committing an offense exist. In Brazil, for example, drivers that are not caught in contravention with transit regulations during the current year have a discount in the cost of the car annual permit. Thus, crime prevention has as its main arguments the risk of punishment and its real application if the offense is committed. ∗ Corresponding author at: Instituto de Fsica, UFRGS, Caixa Postal 15051, 91501-970 Porto Alegre, RS, Brazil. E-mail addresses: roberto@if.ufrgs.br (J.R. Iglesias), vika.semeshenko@gmail.com (V. Semeshenko), schneider.eder@gmail.com (E.M. Schneider), mirta.gordon@imag.fr (M.B. Gordon). 0378-4371/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.physa.2012.03.001