Baston, V.J. and Garnaev, A.Y.
A search game with a protector.
Naval Research Logistics, 47, (2), . (doi:10.1002/(SICI)1520-6750(200003)47:2<85::AID-NAV1>3.0.CO;2-C).
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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 (-ixi)) exp (-iyi) when the searcher and protector allocate resources xi and yi respectively to point i. An algorithm to find this Nash equilibrium is given.
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