A search game with a protector
Baston, V.J. and Garnaev, A.Y. (2000) A search game with a protector. Naval Research Logistics, 47, (2), 85-96. (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.
|Keywords:||search game, nonzero sum game, Nash equilibrium|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||University Structure - Pre August 2011 > School of Mathematics > Operational Research
|Date Deposited:||20 Jul 2006|
|Last Modified:||01 Jun 2011 11:29|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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