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A competitive search game with a moving target

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  • Duvocelle, Benoit
  • Flesch, János
  • Staudigl, Mathias
  • Vermeulen, Dries

Abstract

We introduce a discrete-time search game, in which two players compete to find an invisible object first. The object moves according to a time-varying Markov chain on finitely many states. The players are active in turns. At each period, the active player chooses a state. If the object is there then he finds the object and wins. Otherwise the object moves and the game enters the next period. We show that this game admits a value, and for any error-term ε>0, each player has a pure (subgame-perfect) ε-optimal strategy. Interestingly, a 0-optimal strategy does not always exist. We derive results on the analytic and structural properties of the value and the ε-optimal strategies. We devote special attention to the important time-homogeneous case, where we show that (subgame-perfect) optimal strategies exist if the Markov chain is irreducible and aperiodic.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:303:y:2022:i:2:p:945-957
    DOI: 10.1016/j.ejor.2022.03.004
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    Cited by:

    1. 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.
    2. Steve Alpern & Li Zeng, 2022. "Social Distancing, Gathering, Search Games: Mobile Agents on Simple Networks," Dynamic Games and Applications, Springer, vol. 12(1), pages 288-311, March.
    3. 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.

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