2023-06332 - Post-Doctoral Research Visit F/M Application of Stackelberg games to deter crime and improve security perception in urban areas

Contract type : Fixed-term contract

Level of qualifications required : PhD or equivalent

Fonction : Post-Doctoral Research Visit

About the research centre or Inria department

The Inria University of Lille centre, created in 2008, employs 360 people including 305 scientists in 15 research teams. Recognised for its strong involvement in the socio-economic development of the Hauts-De-France region, the Inria University of Lille centre pursues a close relationship with large companies and SMEs. By promoting synergies between researchers and industrialists, Inria participates in the transfer of skills and expertise in digital technologies and provides access to the best European and international research for the benefit of innovation and companies, particularly in the region.

For more than 10 years, the Inria University of Lille centre has been located at the heart of Lille's university and scientific ecosystem, as well as at the heart of Frenchtech, with a technology showroom based on Avenue de Bretagne in Lille, on the EuraTechnologies site of economic excellence dedicated to information and communication technologies (ICT).


Every year Inria International Relations Department has a few postdoctoral positions in order to support Inria international collaborations.

This year, postdoctoral positions within the frame of Inria London, Inria Brasil and Inria Chile programs and to strengthen partnerships with Simula (Norway), University of Waterloo (Canada) and KAIST and ETRI (South Korea) are eligible.

The postdoc contract will have a duration of 12 to 24 months. The default start date is November 1st, 2023 and not later than January, 1st 2024. The postdoctoral fellow will be recruited by one of the Inria Centers in France but it is recommended that the time is shared between France and the partner’s country (please note that the postdoctoral fellow has to start his/her  contract being in France and that the visits have to respect Inria rules for missions)


Candidates for postdoctoral positions are recruited after the end of their  Ph.D. or after a first post-doctoral period: for the candidates who obtained their PhD in the Northern hemisphere, the date of the Ph.D. defense shall be later than 1 September 2021; in the Southern hemisphere, later than 1 April 2021.

In order to encourage mobility, the postdoctoral position  must take place in a scientific environment that is truly different from the one of the Ph.D. (and, if applicable, from the position held since the Ph.D.); particular attention is thus paid to French or international candidates who obtained their doctorate abroad.

Main activities

Crime is primarily an urban phenomenon that in recent decades has increased in Latin America due to rapid urban growth (Cheng and Chen (2021)). According to the UN (Un-Habitat (2012)) 60% of urban inhabitants in Latin American countries have been victims of crime and the victimization rate has reached 70% in some cities. In Chile, 32% of households had a member who was a victim of robbery or attempted robbery, and 28% of the population has a high level of fear (Ciudadana (2022)). Urban safety refers to crime prevention practices, their implementation, and the public perception of crime. A mismatch between fear of crime and crime rates is not uncommon (Ciudadana (2022), Killias and Clerici (2000), Borooah and Carcach (1997), Doeksen (1997)). Thus, the mechanisms that the police authority implement to deter crime in urban areas must not only be effective but must also improve citizens’ perception of safety.


Police authority has a limited number of operational mechanisms to deter urban crime and improve the perception of security in urban areas. These mechanisms are mainly based on crime analysis, defined as ”the set of systematic and analytical processes that provide timely and relevant information on crime patterns and correlations between crime trends” (Wortley and Townsley (2016)). Two mechanisms are distinguished. (1) The first one is the crime analysis of hotspot mapping. Crime hotspots are small geographic areas with high rates of criminal activity (Weisburd and Telep (2014)). According to Weisburd (2015), these hotspots tend to remain spatially and temporally, and consequently, crime can be mitigated through proper data collection. There are several methods for mapping crime hotspots such as kernel density estimation (KDE) that allows the calculation of the probability density function of crime incidents (Hu et al. (2018)). (2) The second one is the deployment of police resources through police patrols. The objective of police patrols is to provide police services to prevent crime (Novak et al. (2016)) and respond more quickly to crime incidence. Thus, the police authority, based on a risk surface that suggests where crime events have been previously clustered (hotspot mapping), defines a patrolling strategy that consists of determining the frequency with which hotspots should be patrolled. A patrol strategy can be operationally implemented through a set of patrol schedules, where each schedule is a collection of temporal-spatial patrol paths (one for each police patrol) with an associated probability of being selected, denoted as unpredictable patrolling schedule. The objective of a patrol strategy and the unpredictable patrol schedule is to deter the greatest number of offenders and increase citizens’ perception of safety.

The problem of determining the frequency of hotspot patrolling can be viewed as a Stackelberg game in which the police authority establishes a time-space distribution of patrol probabilities at hotspots, and criminals choose where to commit a crime based on their knowledge of being caught by the police authority. Similarly, the unpredictable patrolling schedule can be viewed as a Stackelberg game in which the police authority establishes the set of patrol paths and their respective probabilities of being selected while criminals respond by optimizing their objective function given the probability of being caught. To the best of our knowledge, only Espejo et al. (2016) have modeled the interaction between police forces and offenders in urban areas under a Stackelberg game approach. However, they address the problem of allocating police officers in a bounded urban area to deter criminal action.


Patrolling strategies and unpredictable patrolling schedules in urban areas are particular topics of security games (SG). SG has been successfully applied in security domains to generate unpredictable patrol strategies, e.g., to protect flights (Tambe (2011)), for counter-terrorism and fare evasion controls (Brotcorne et al. (2021)). However, compared to strategic attackers (such as terrorists), who execute a well-laid plan, criminals in urban areas are less strategic in planning attacks and more flexible in executing well-laid plans based on their knowledge of police patrols or allocation. Thus, the main challenge in this area is to model the behavior of urban criminals (Zhang et al. (2016)).


This project aims to address the patrolling strategy and unpredictable patrol scheduling to deter crime and improve the perception of safety in urban areas from the point of view of the Stackelberg game, taking into account realistic models for the reaction of urban criminals, realistic models for the actions of the police authority, and guaranteeing the quality of the solutions in terms of the optimality gap. Thus, the expected result of the project are practical and novel mathematical tools to define patrolling strategies and unpredictable patrol scheduling in urban areas to deter the most significant number of urban criminals.



V. K. Borooah and C. A. Carcach. Crime and fear: Evidence from australia. The British Journal of Criminology, 37(4): 635–657, 1997.

L. Brotcorne, P. Escalona, B. Fortz, and M. Labbé. Fare inspection patrols scheduling in transit systems using a stackelberg game approach. Transportation Research Part B: Methodological, 154:1–20, 2021.

T. Cheng and T. Chen. Urban crime and security. Urban Informatics, pages 213–228, 2021. F. P. Ciudadana. Índice paz ciudadana 2022, 2022. URL https://pazciudadana.cl/wp-content/uploads/2022/10/ Presentacion-IFPC-2022-1.pdf. H. Doeksen. Reducing crime and the fear of crime by reclaiming new zealand’s suburban street. Landscape and urban planning, 39(2-3):243–252, 1997.

G. Espejo, G. L’HUILLIER, and R. Weber. A game-theoretical approach for policing decision support. European Journal of Applied Mathematics, 27(3):338–356, 2016.

Y. Hu, F. Wang, C. Guin, and H. Zhu. A spatio-temporal kernel density estimation framework for predictive crime hotspot mapping and evaluation. Applied geography, 99:89–97, 2018.

M. Killias and C. Clerici. Different measures of vulnerability in their relation to different dimensions of fear of crime. British journal of criminology, 40(3):437–450, 2000.

K. J. Novak, A. M. Fox, C. M. Carr, and D. A. Spade. The efficacy of foot patrol in violent places. Journal of Experimental Criminology, 12:465–475, 2016.

M. Tambe. Security and game theory: algorithms, deployed systems, lessons learned. Cambridge university press, 2011. Un-Habitat. Enhancing urban safety and security: Global report on human settlements 2007. Routledge, 2012.

D. Weisburd. The law of crime concentration and the criminology of place. Criminology, 53(2):133–157, 2015.

D. Weisburd and C. W. Telep. Hot spots policing: What we know and what we need to know. Journal of Contemporary Criminal Justice, 30(2):200–220, 2014.

R. Wortley and M. Townsley. Environmental criminology and crime analysis: Situating the theory, analytic approach and application. In Environmental criminology and crime analysis, pages 20–45. Routledge, 2016.

C. Zhang, S. Gholami, D. Kar, A. Sinha, M. Jain, R. Goyal, and M. Tambe. Keeping pace with criminals: An extended study of designing patrol allocation against adaptive opportunistic criminals. Games, 7(3):15, 2016.


Good knowledges in:

  • Optimization
  • Statistics
  • Algorithmic
  • Code in C++, Pytthon 

Benefits package

  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
  • Possibility of teleworking and flexible organization of working hours
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training
  • Social security coverage


Gross salary : 2746 € by month