A search game with a protector

V.J. Baston and A.Y. Garnaev

Naval Research Logistics (NRL), 2000, vol. 47, issue 2, 85-96

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

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:wly:navres:v:47:y:2000:i:2:p:85-96

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