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Accumulation Games, Part 1: Noisy Search

Author

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  • K. Kikuta

    (Toyama University)

  • W. H. Ruckle

    (Clemson University)

Abstract

In an accumulation game, a hider places objects at locations, and a seeker examines these locations. If the seeker discovers an object, the seeker confiscates it. The goal of the hider is to accumulate a certain number of objects before a given time, and the goal of the seeker is to prevent this. In this paper, we first classify various possible variations on the accumulation game. Next, we discuss the so-called noisy accumulation game in which the hider can observe each action of the seeker. We present the solution of this game for all but some marginal cases and illustrate it with computational examples.

Suggested Citation

  • K. Kikuta & W. H. Ruckle, 1997. "Accumulation Games, Part 1: Noisy Search," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 395-408, August.
    • Handle: RePEc:spr:joptap:v:94:y:1997:i:2:d:10.1023_a:1022639813629
    DOI: 10.1023/A:1022639813629
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    References listed on IDEAS

    as
    1. William H. Ruckle, 1992. "The reporting time problem: Integration of intelligence with verification," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(7), pages 893-903, December.
    2. William H. Ruckle, 1992. "The Upper Risk of an Inspection Agreement," Operations Research, INFORMS, vol. 40(5), pages 877-884, October.
    3. Garnaev, Andrej Yu, 1992. "On Simple MIX Game," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(3), pages 237-247.
    4. Kensaku Kikuta & William H. Ruckle, 1994. "Initial point search on weighted trees," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(6), pages 821-831, October.
    5. Garnaev, A Yu, 1992. "A Remark on the Princess and Monster Search Game," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 269-276.
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    Cited by:

    1. N. Zoroa & M. J. Fernández-Sáez & P. Zoroa, 1999. "A Game Related to the Number of Hides Game," Journal of Optimization Theory and Applications, Springer, vol. 103(2), pages 457-473, November.
    2. Dömötör Pálvölgyi, 2018. "All or Nothing Caching Games with Bounded Queries," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-9, March.
    3. Steve Alpern & Robbert Fokkink & Christos Pelekis, 2012. "A Proof of the Kikuta–Ruckle Conjecture on Cyclic Caching of Resources," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 650-661, June.
    4. Oléron Evans, Thomas P. & Bishop, Steven R., 2013. "Static search games played over graphs and general metric spaces," European Journal of Operational Research, Elsevier, vol. 231(3), pages 667-689.
    5. 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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    Keywords

    Zero-sum games; search games;

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