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Search for a moving target in a competitive environment

Author

Listed:
  • Benoit Duvocelle

    (Maastricht University)

  • János Flesch

    (Maastricht University)

  • Hui Min Shi

    (Maastricht University)

  • Dries Vermeulen

    (Maastricht University)

Abstract

We consider a discrete-time dynamic search game in which a number of players compete to find an invisible object that is moving according to a time-varying Markov chain. We examine the subgame perfect equilibria of these games. The main result of the paper is that the set of subgame perfect equilibria is exactly the set of greedy strategy profiles, i.e. those strategy profiles in which the players always choose an action that maximizes their probability of immediately finding the object. We discuss various variations and extensions of the model.

Suggested Citation

  • Benoit Duvocelle & János Flesch & Hui Min Shi & Dries Vermeulen, 2021. "Search for a moving target in a competitive environment," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 547-557, June.
    • Handle: RePEc:spr:jogath:v:50:y:2021:i:2:d:10.1007_s00182-021-00761-5
    DOI: 10.1007/s00182-021-00761-5
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    References listed on IDEAS

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    1. Duvocelle, Benoit & Flesch, János & Staudigl, Mathias & Vermeulen, Dries, 2022. "A competitive search game with a moving target," European Journal of Operational Research, Elsevier, vol. 303(2), pages 945-957.
    2. Koller, Daphne & Megiddo, Nimrod & von Stengel, Bernhard, 1996. "Efficient Computation of Equilibria for Extensive Two-Person Games," Games and Economic Behavior, Elsevier, vol. 14(2), pages 247-259, June.
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    4. János Flesch & Emin Karagözoǧlu & Andrés Perea, 2009. "Optimal search for a moving target with the option to wait," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(6), pages 526-539, September.
    5. Stanley J. Benkoski & Michael G. Monticino & James R. Weisinger, 1991. "A survey of the search theory literature," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(4), pages 469-494, August.
    6. Garrec, Tristan & Scarsini, Marco, 2020. "Search for an immobile hider on a stochastic network," European Journal of Operational Research, Elsevier, vol. 283(2), pages 783-794.
    7. Bogdan C. Bichescu & Michael J. Fry, 2009. "Vendor-managed inventory and the effect of channel power," Springer Books, in: Herbert Meyr & Hans-Otto Günther (ed.), Supply Chain Planning, pages 247-280, Springer.
    8. Tobias Harks & Max Klimm, 2012. "On the Existence of Pure Nash Equilibria in Weighted Congestion Games," Mathematics of Operations Research, INFORMS, vol. 37(3), pages 419-436, August.
    9. Rahul Savani & Bernhard Stengel, 2006. "Hard-to-Solve Bimatrix Games," Econometrica, Econometric Society, vol. 74(2), pages 397-429, March.
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    Cited by:

    1. Duvocelle, Benoit & Flesch, János & Staudigl, Mathias & Vermeulen, Dries, 2022. "A competitive search game with a moving target," European Journal of Operational Research, Elsevier, vol. 303(2), pages 945-957.
    2. Mikhail Khachumov & Vyacheslav Khachumov, 2023. "Modeling the Solution of the Pursuit–Evasion Problem Based on the Intelligent–Geometric Control Theory," Mathematics, MDPI, vol. 11(23), pages 1-26, December.

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