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A search game with a protector

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  • V.J. Baston
  • A.Y. Garnaev

Abstract

A classic problem in Search Theory is one in which a searcher allocates resources to the points of the integer interval [1, n] in an attempt to find an object which has been hidden in them using a known probability function. In this paper we consider a modification of this problem in which there is a protector who can also allocate resources to the points; allocating these resources makes it more difficult for the searcher to find an object. We model the situation as a two‐person non‐zero‐sum game so that we can take into account the fact that using resources can be costly. It is shown that this game has a unique Nash equilibrium when the searcher's probability of finding an object located at point i is of the form (1 − exp (−λixi)) exp (−μiyi) when the searcher and protector allocate resources xi and yi respectively to point i. An algorithm to find this Nash equilibrium is given. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47:85–96, 2000

Suggested Citation

  • V.J. Baston & A.Y. Garnaev, 2000. "A search game with a protector," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(2), pages 85-96, March.
    • Handle: RePEc:wly:navres:v:47:y:2000:i:2:p:85-96
    DOI: 10.1002/(SICI)1520-6750(200003)47:23.0.CO;2-C
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    References listed on IDEAS

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    1. John S. Croucher, 1975. "Application of the fundamental theorem of games to an example concerning antiballistic missile defense," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 22(1), pages 197-203, March.
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    Cited by:

    1. A. Garnaev, 2007. "Technical note: Find a hidden “treasure”," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(1), pages 109-114, February.

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    1. A. Garnaev, 2007. "Technical note: Find a hidden “treasure”," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(1), pages 109-114, February.
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