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A sequential Stackelberg game for dynamic inspection problems

Author

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  • Guzmán, Cristóbal
  • Riffo, Javiera
  • Telha, Claudio
  • Van Vyve, Mathieu

Abstract

We introduce an inspection game where one inspector has the role of monitoring a group of inspectees. The inspector has the resources to visit only a few of them. Visits are performed sequentially with no repetitions. The inspectees report and share the sequence of inspections as they occur, but otherwise, they do not cooperate. We formulate two Stackelberg models, a static game where the inspector commits to play a sequence of visits announced at the start of the game, and a dynamic game where visits will depend on who was visited previously. In the static game, we characterize the (randomized) inspection paths in an equilibrium using linear programs. In the dynamic game, we determine the inspection paths in an equilibrium using backward induction.

Suggested Citation

  • Guzmán, Cristóbal & Riffo, Javiera & Telha, Claudio & Van Vyve, Mathieu, 2022. "A sequential Stackelberg game for dynamic inspection problems," European Journal of Operational Research, Elsevier, vol. 302(2), pages 727-739.
    • Handle: RePEc:eee:ejores:v:302:y:2022:i:2:p:727-739
    DOI: 10.1016/j.ejor.2021.12.015
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    1. Gilboa, Itzhak & Zemel, Eitan, 1989. "Nash and correlated equilibria: Some complexity considerations," Games and Economic Behavior, Elsevier, vol. 1(1), pages 80-93, March.
    2. Luciano Andreozzi, 2004. "Rewarding Policemen Increases Crime. Another Surprising Result from the Inspection Game," Public Choice, Springer, vol. 121(1), pages 69-82, October.
    3. Stamatios Katsikas & Vassili Kolokoltsov & Wei Yang, 2016. "Evolutionary Inspection and Corruption Games," Games, MDPI, vol. 7(4), pages 1-25, October.
    4. Gustav Feichtinger, 1983. "A Differential Games Solution to a Model of Competition Between a Thief and the Police," Management Science, INFORMS, vol. 29(6), pages 686-699, June.
    5. Manish Jain & Jason Tsai & James Pita & Christopher Kiekintveld & Shyamsunder Rathi & Milind Tambe & Fernando Ordóñez, 2010. "Software Assistants for Randomized Patrol Planning for the LAX Airport Police and the Federal Air Marshal Service," Interfaces, INFORMS, vol. 40(4), pages 267-290, August.
    6. Marlin U. Thomas & Yair Nisgav, 1976. "An infiltration game with time dependent payoff," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 23(2), pages 297-302, June.
    7. von Stengel, Bernhard & Zamir, Shmuel, 2010. "Leadership games with convex strategy sets," Games and Economic Behavior, Elsevier, vol. 69(2), pages 446-457, July.
    8. Magat, Wesley A & Viscusi, W Kip, 1990. "Effectiveness of the EPA's Regulatory Enforcement: The Case of Industrial Effluent Standards," Journal of Law and Economics, University of Chicago Press, vol. 33(2), pages 331-360, October.
    9. Alan Washburn & Kevin Wood, 1995. "Two-Person Zero-Sum Games for Network Interdiction," Operations Research, INFORMS, vol. 43(2), pages 243-251, April.
    10. José Correa & Tobias Harks & Vincent J. C. Kreuzen & Jannik Matuschke, 2017. "Fare Evasion in Transit Networks," Operations Research, INFORMS, vol. 65(1), pages 165-183, February.
    11. V. J. Baston & F. A. Bostock, 1991. "A generalized inspection game," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(2), pages 171-182, April.
    12. Michael Maschler, 1966. "A price leadership method for solving the inspector's non‐constant‐sum game," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 13(1), pages 11-33, March.
    13. John Canty, Morton & Rothenstein, Daniel & Avenhaus, Rudolf, 2001. "Timely inspection and deterrence," European Journal of Operational Research, Elsevier, vol. 131(1), pages 208-223, May.
    14. Reinganum, Jennifer F & Wilde, Louis L, 1986. "Equilibrium Verification and Reporting Policies in a Model of Tax Compliance," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(3), pages 739-760, October.
    15. Thomas S. Ferguson & Costis Melolidakis, 1998. "On the inspection game," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(3), pages 327-334, April.
    16. George Tsebelis, 1990. "Penalty has no Impact on Crime:," Rationality and Society, , vol. 2(3), pages 255-286, July.
    17. Bucarey L., Víctor & Casorrán, Carlos & Labbé, Martine & Ordoñez, Fernando & Figueroa, Oscar, 2021. "Coordinating resources in Stackelberg Security Games," European Journal of Operational Research, Elsevier, vol. 291(3), pages 846-861.
    18. Conitzer, Vincent & Sandholm, Tuomas, 2008. "New complexity results about Nash equilibria," Games and Economic Behavior, Elsevier, vol. 63(2), pages 621-641, July.
    19. José Correa & Tobias Harks & Vincent J. C. Kreuzen & Jannik Matuschke, 2017. "Fare Evasion in Transit Networks," Operations Research, INFORMS, vol. 65(1), pages 165-183, February.
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