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All or Nothing Caching Games with Bounded Queries

Author

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  • Dömötör Pálvölgyi

    (Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, UK)

Abstract

We determine the value of some search games where our goal is to find all of some hidden treasures using queries of bounded size. The answer to a query is either empty, in which case we lose, or a location, which contains a treasure. We prove that if we need to find d treasures at n possible locations with queries of size at most k, then our chance of winning is kd n d if each treasure is at a different location and kd n+d−1 d if each location might hide several treasures for large enough n. Our work builds on some results by Csóka who has studied a continuous version of this problem, known as Alpern’s Caching Game we also prove that the value of Alpern’s Caching Game is kd n+d−1 d for integer k and large enough n.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:igtrxx:v:20:y:2018:i:01:n:s0219198917500232
    DOI: 10.1142/S0219198917500232
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

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