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Continuous accumulation games on discrete locations

Author

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  • Kensaku Kikuta
  • William H. Ruckle

Abstract

In an accumulation game, a HIDER attempts to accumulate a certain number of objects or a certain quantity of material before a certain time, and a SEEKER attempts to prevent this. In a continuous accumulation game the HIDER can pile material either at locations $1, 2, …, n, or over a region in space. The HIDER will win (payoff 1) it if accumulates N units of material before a given time, and the goal of the SEEKER will win (payoff 0) otherwise. We assume the HIDER can place continuous material such as fuel at discrete locations i = 1, 2, …, n, and the game is played in discrete time. At each time k > 0 the HIDER acquires h units of material and can distribute it among all of the locations. At the same time, k, the SEEKER can search a certain number s

Suggested Citation

  • Kensaku Kikuta & William H. Ruckle, 2002. "Continuous accumulation games on discrete locations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(1), pages 60-77, February.
    • Handle: RePEc:wly:navres:v:49:y:2002:i:1:p:60-77
    DOI: 10.1002/nav.1048
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    References listed on IDEAS

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    1. W. H. Ruckle & K. Kikuta, 2000. "Continuous Accumulation Games in Continuous Regions," Journal of Optimization Theory and Applications, Springer, vol. 106(3), pages 581-601, September.
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    Cited by:

    1. Bastián Bahamondes & Mathieu Dahan, 2024. "Hide-and-Seek Game with Capacitated Locations and Imperfect Detection," Decision Analysis, INFORMS, vol. 21(2), pages 110-124, June.
    2. Steve Alpern & Alec Morton & Katerina Papadaki, 2011. "Patrolling Games," Operations Research, INFORMS, vol. 59(5), pages 1246-1257, October.
    3. Endre Csóka & Thomas Lidbetter, 2016. "The solution to an open problem for a caching game," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(1), pages 23-31, February.

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