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A game-theoretical approach for policing decision support

Published online by Cambridge University Press:  14 September 2015

G. ESPEJO ,
G. L'HUILLIER  and
R. WEBER
G. ESPEJO
Affiliation:
Department of Industrial Engineering, FCFM, Universidad de Chile, Av. República 701, Santiago, Chile email: juespejo@ing.uchile.cl, rweber@dii.uchile.cl
G. L'HUILLIER
Affiliation:
Wifi Securities, Inc., 998 Hamilton Ave, Menlo Park, CA, 94025, USA email: g@zapship.com
R. WEBER
Affiliation:
Department of Industrial Engineering, FCFM, Universidad de Chile, Av. República 701, Santiago, Chile email: juespejo@ing.uchile.cl, rweber@dii.uchile.cl
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Abstract

Recently, many security-related problems have gained increasing attention from a quantitative perspective. In this paper, we propose a game-theoretical approach to model the interaction between police forces and delinquents in public places. In the well-known Stackelberg game, a leader is faced with only one follower. However, in our application, the police are simultaneously faced with many offenders, who may be organized or act independently of each other. This application motivates the development of two games: a classical leader-follower interaction between police and organized criminals on the one hand and a novel approach between the leader and selfishly acting offenders on the other. It is of special interest that the effect of crime displacement under police surveillance be anticipated by the proposed models. Results using data from a simulated environment emphasise how these models can provide decision support for policing outperforming traditional strategies.

Keywords

91A40 Game-theoretic models91A80 Applications of game theory78M50 Optimisation
Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Issue 3: Mathematical Modelling of Crime and Security , June 2016 , pp. 338 - 356
Copyright
Copyright © Cambridge University Press 2015 

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References

[1]Anselin, L., Cohen, J., Cook, F., Gorr, W., & Tita, G. (2000) Spatial analyses of crime. Criminal Justice 4, 213–262.Google Scholar
[2]Becker, G. S. (1968) Crime and punishment: An economic approach. J. Political Economy 76, 169–217.CrossRefGoogle Scholar
[3]Berestycki, H., Johnson, S. D., Ockendon, R. & Primicerio, M. (2010) Foreword to the special issue of ejam on crime modelling. Eur. J. Appl. Math. 21, 271–274.Google Scholar
[4]Bier, V., Oliveros, S. & Samuelson, L. (2007) Choosing what to protect: Strategic defensive allocation against an unknown attacker. J. Public Econ. Theory 9 (4), 563–587.CrossRefGoogle Scholar
[5]Braga, A. (2001) The effects of hot spots policing on crime. Ann. Am. Political Soc. Sci. 578, 104–125.Google Scholar
[6]Brantingham, P. L. & Brantingham, P. J. (1982) Mobility, notoriety, and crime: A study in the crime patterns of urban nodal points. J. Environ. Syst. 11 (1), 89–99.Google Scholar
[7]Cantrell, R. S., Cosner, C. & Manasevich, R. (2012) Global bifurcation of solutions for crime modeling equations. SIAM J. Math. Anal. 44 (3), 1340–1358.CrossRefGoogle Scholar
[8]Clarke, R. V. (1980) Situational crime prevention: Theory and practice. Br. J.Criminology 20, 136–147.Google Scholar
[9]Clarke, R. V. & Cornish, R. B. (2008) The rational choice perspective. In: Wortley, R. & Mazzerole, L. (editors), Environmental Criminology and Crime Analysis, Willan Publishing, New York, pp. 21–47.Google Scholar
[10]Cressman, R. & Krivan, V. (2006) Migration dynamics for the ideal free distribution. Am. Naturalist 168, 384–425.Google Scholar
[11]Devia, N. & Weber, R. (2013) Generating crime data using agent-based simulation. Comput. Environ. Urban Syst. 42, 26–41.CrossRefGoogle Scholar
[12]Di Tella, R. & Schargrodsky, E. (2004) Do police reduce crime? estimates using the allocation of police forces after a terrorist attack. Am. Econ. Rev. 94, 115–133.Google Scholar
[13]D'Orsogna, M. R. & Perc, M. (2015) Statistical physics of crime: A review. Phys. Life Rev. 12, 1–21.Google Scholar
[14]D'Orsogna, M. R., Kendall, R., McBride, M. & Short, M. B. (2013) Criminal defectors lead to the emergence of cooperation in an experimental, adversarial game. PLoS ONE 8 (4), e61458.CrossRefGoogle Scholar
[15]Felson, M. (2010) What every mathematician should know about modelling crime. Eur. J. Appl. Math. 21, 275–281.Google Scholar
[16]Garoupa, N. (1997) The theory of optimal law enforcement. J. Econ. Sur. 11, 267–295.Google Scholar
[17]Gibbons, R. (1992) Game Theory for Applied Economists, Princeton University Press, Princeton, New Jersey.Google Scholar
[18]Hausken, K. (2010) Defense and attack of complex and dependent systems. Reliab. Eng. Syst. Saf. 95, 29–42.Google Scholar
[19]Helbing, D., Brockmann, D., Chadefaux, Th., Donnay, K., Blanke, U., Woolley-Meza, O., Moussaid, M., Johansson, A., Krause, J., Schutte, S. & Perc, M. (2015) Saving human lives: What complexity science and information systems can contribute. J. Stat. Phys. 158, 735–781.Google Scholar
[20]Jain, M., Tsai, J., Pita, J., Kiekintveld, C., Rathi, S., Tambe, M. & Ordónez, F. (2010) Software assistants for randomized patrol planning for the lax airport police and the federal air marshal service. Interfaces 40 (4), 267–290.CrossRefGoogle Scholar
[21]Johnson, S. D. (2010) A brief history of the analysis of crime concentration. Eur. J. Appl. Math. 21, 349–370.Google Scholar
[22]Korzhyk, D., Yin, Z., Kiekintveld, C., Conitzer, C. & Tambe, M. (2011) Stackelberg versus nash in security games: An extended investigation of interchangeability, equivalence, and uniqueness. J. Artif. Intell. Res. 41, 297–327.Google Scholar
[23]Krivan, V., Cressman, R. & Schneider, C. (2008) The ideal free distribution: A review and synthesis of the game-theoretic perspective. Theor. Population Biol. 73, 403–425.Google Scholar
[24]Lin, M.-J. (2009) More police, less crime: Evidence from U.S. state data. Int. Rev. Law Econ. 29, 73–80.Google Scholar
[25]Manasevich, R., Phan, Q. H. & Souplet, P. (2013) Global existence of solutions for a chemotaxis-type system arising in crime modelling. Eur. J. Appl. Math. 24, 273–296.Google Scholar
[26]Nagin, D. (1998) Criminal deterrence research at the outset of the twenty-first century. Crime and Justice 23, 1–42.Google Scholar
[27]Offerman, T. (1997) Beliefs and Decision Rules in Public Good Games, Springer, US.CrossRefGoogle Scholar
[28]Perc, M., Donnay, K. & Helbing, D. (2013) Understanding recurrent crime as system-immanent collective behavior. PLoS ONE 8, 1–7.CrossRefGoogle ScholarPubMed
[29]Perc, M. & Szolnoki, A. (2015) A double-edged sword: Benefits and pitfalls of heterogeneous punishment in evolutionary inspection games. Sci. Rep. 5, 1–11.Google Scholar
[30]Riccio, L. (1974) Direct deterrence - an analysis of the effectiveness of police patrol and other crime prevention technologies. J. Criminal Justice 2, 207–217.Google Scholar
[31]Roughgarden, T. & Tardos, E. (2007) Introduction to the inefficiency of equilibria. In: Nisan, N., Roughgarden, T., Tardos, E. & Vazirani, V. (editors), Algorithmic Game Theory, Cambridge University Press, Cambridge, pp. 443–460.Google Scholar
[32]Sandholm, W. H. (2007) Population Games and Evolutionary Dynamics, The MIT Press, Cambridge.Google Scholar
[33]Sherali, H. D., Soyster, A. L. & Murphy, F. H. (1983) Stackelberg-nash-cournot equilibria: Characterizations and computations. Oper. Res. 32 (2), 253–276.CrossRefGoogle Scholar
[34]Sherman, L. W., Gottfredson, D., MacKenzie, D., Eck, E., Reuter, P. & Bushway, S. (1997) Preventing crime: What works, what doesn't, what's promising. A report to the united states congress. Technical report, University of Maryland, Department of Criminology and Criminal Justice.CrossRefGoogle Scholar
[35]Short, M. B., Bertozzi, A. L. & Brantingham, P. J. (2010) Nonlinear patterns in urban crime: Hotspots, bifurcations, and suppression. SIAM J. Appl. Dyn. Syst. 9 (2), 462–483.Google Scholar
[36]Short, M. B., Brantingham, P. J., Bertozzi, A. L. & Tita, G. E. (2010) Dissipation and displacement of hotspots in reaction-diffusion models of crime. Proc. Natl. Acad. Sci. USA 107 (9), 3961–3965.Google Scholar
[37]Short, M. B., Brantingham, P. J. & D'Orsogna, M. R. (2010) Cooperation and punishment in an adversarial game: How defectors pave the way to a peaceful society. Phys. Rev. E 82 066114, 1–7.Google Scholar
[38]Short, M. B., Pitcher, A. B. & D'Orsogna, M. R. (2013) External conversions of player strategy in an evolutionary game: A cost-benefit analysis through optimal control. Eur. J. Appl. Math. 24, 131–159.Google Scholar
[39]Smith, D. (1962) Random patrol: An application of game theory to police problems. J. Criminal Law, Criminology Police Sci. 53 (2), 258–263.CrossRefGoogle Scholar
[40]Sutherland, E. H. (1947) Principles of Criminology, J.B. Lippincott Co., Chicago, Philadelphia.Google Scholar
[41]Tambe, M. (editor) (2012) Security and Game Theory - Algorithms, Deployed Systems, Lessons Learned, Cambridge University Press, New York.Google Scholar
[42]von Stackelberg, H. F. (1934) Marktform und Gleichgewicht, Julius Springer, Vienna.Google Scholar
[43]Weisburd, D. & Eck, J. E. (2004) What can police do to reduce crime, disorder, and fear? Ann. Am. Acad. Political Soc. Sci. 593, 42–65.Google Scholar
[44]Worrall, J. L. and Kovandzic, T. V. (2010) Police levels and crime rates: An instrumental variables approach. Soc. Sci. Res. 39, 506–516.Google Scholar