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Determining all Nash equilibria in a (bi-linear) inspection game

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  • Deutsch, Yael
  • Golany, Boaz
  • Rothblum, Uriel G.

Abstract

This paper addresses a "game" between an inspection agency and multiple inspectees that are subject to random inspections by that agency. We provide explicit (easily computable) expressions for all possible Nash equilibria and verify that none is left out. In particular, our results characterize situations when there exists a unique Nash equilibrium. We also explore special features of the Nash equilibria and the solution of the problem the inspection agency faces in a non-strategic environment.

Suggested Citation

  • Deutsch, Yael & Golany, Boaz & Rothblum, Uriel G., 2011. "Determining all Nash equilibria in a (bi-linear) inspection game," European Journal of Operational Research, Elsevier, vol. 215(2), pages 422-430, December.
    • Handle: RePEc:eee:ejores:v:215:y:2011:i:2:p:422-430
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    References listed on IDEAS

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    Cited by:

    1. Johnston, Iain G., 2022. "Optimal strategies in the fighting fantasy gaming system: Influencing stochastic dynamics by gambling with limited resource," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1272-1281.
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    3. Yael Deutsch & Boaz Golany, 2016. "Multiple agents finitely repeated inspection game with dismissals," Annals of Operations Research, Springer, vol. 237(1), pages 7-26, February.
    4. Fandel, G. & Trockel, J., 2013. "Avoiding non-optimal management decisions by applying a three-person inspection game," European Journal of Operational Research, Elsevier, vol. 226(1), pages 85-93.
    5. Avenhaus, Rudolf & Krieger, Thomas, 2013. "Distributing inspections in space and time – Proposed solution of a difficult problem," European Journal of Operational Research, Elsevier, vol. 231(3), pages 712-719.
    6. Hunt, Kyle & Zhuang, Jun, 2024. "A review of attacker-defender games: Current state and paths forward," European Journal of Operational Research, Elsevier, vol. 313(2), pages 401-417.
    7. Yael Deutsch & Boaz Golany, 2019. "Securing Gates of a Protected Area: A Hybrid Game and Queueing Theory Modeling Approach," Decision Analysis, INFORMS, vol. 16(1), pages 31-45, March.
    8. Fatima Khanchouche & Samir Sbabou & Hatem Smaoui & Ziad Abderrahmane, 2023. "Congestion Games with Player-Specific Payoff Functions: The Case of Two Resources, Computation and Algorithms. First version," Economics Working Paper Archive (University of Rennes & University of Caen) 2023-08, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    9. Deutsch, Yael & Goldberg, Noam & Perlman, Yael, 2019. "Incorporating monitoring technology and on-site inspections into an n-person inspection game," European Journal of Operational Research, Elsevier, vol. 274(2), pages 627-637.
    10. Yael Deutsch & Boaz Golany & Noam Goldberg & Uriel G. Rothblum, 2013. "Inspection games with local and global allocation bounds," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(2), pages 125-140, March.
    11. Jann, Ole & Schottmüller, Christoph, 2021. "Regime change games with an active defender," Games and Economic Behavior, Elsevier, vol. 129(C), pages 96-113.
    12. Yael Deutsch & Boaz Golany, 2016. "Multiple agents finitely repeated inspection game with dismissals," Annals of Operations Research, Springer, vol. 237(1), pages 7-26, February.
    13. Deutsch, Yael, 2021. "A polynomial-time method to compute all Nash equilibria solutions of a general two-person inspection game," European Journal of Operational Research, Elsevier, vol. 288(3), pages 1036-1052.

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