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A search game on a cyclic graph

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  • Kensaku Kikuta

Abstract

There is a finite cyclic graph. The hider chooses one of all nodes except the specified one, and he hides an (immobile) object there. At the beginning the seeker is at the specified node. After the seeker chooses an ordering of the nodes except the specified one, he examines each nodes in that order until he finds the object, traveling along edges. It costs an amount when he moves from a node to an adjacent one and also when he checks a node. While the hider wishes to maximize the sum of the traveling costs and the examination costs which are required to find the object, the seeker wishes to minimize it. The problem is modeled as a two‐person zero‐sum game. We solve the game when unit costs (traveling cost + examination cost) have geometrical relations depending on nodes. Then we give properties of optimal strategies of both players. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

Suggested Citation

  • Kensaku Kikuta, 2004. "A search game on a cyclic graph," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(7), pages 977-993, October.
    • Handle: RePEc:wly:navres:v:51:y:2004:i:7:p:977-993
    DOI: 10.1002/nav.20025
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    References listed on IDEAS

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    1. Udo Lössner & Ingo Wegener, 1982. "Discrete Sequential Search with Positive Switch Cost," Mathematics of Operations Research, INFORMS, vol. 7(3), pages 426-440, August.
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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. 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.

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