A search game with a protector
A search game with a protector
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.
search game, nonzero sum game, Nash equilibrium
85-96
Baston, V.J.
d6955a5c-e9e9-4ef8-a7d0-70aa54afe998
Garnaev, A.Y.
141a7f4c-075e-456a-a9a0-0aa651b683ef
2000
Baston, V.J.
d6955a5c-e9e9-4ef8-a7d0-70aa54afe998
Garnaev, A.Y.
141a7f4c-075e-456a-a9a0-0aa651b683ef
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 (-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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Published date: 2000
Keywords:
search game, nonzero sum game, Nash equilibrium
Organisations:
Operational Research
Identifiers
Local EPrints ID: 29734
URI: http://eprints.soton.ac.uk/id/eprint/29734
PURE UUID: 09611286-f5f0-4816-be87-59de3b980d4a
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Date deposited: 20 Jul 2006
Last modified: 15 Mar 2024 07:34
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Author:
V.J. Baston
Author:
A.Y. Garnaev
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