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A search game with a protector
Author(s) -
Baston V.J.,
Garnaev A.Y.
Publication year - 2000
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/(sici)1520-6750(200003)47:2<85::aid-nav1>3.0.co;2-c
Subject(s) - nash equilibrium , object (grammar) , computer science , point (geometry) , interval (graph theory) , mathematical economics , game theory , integer (computer science) , search theory , function (biology) , mathematical optimization , mathematics , artificial intelligence , combinatorics , economics , geometry , evolutionary biology , microeconomics , biology , programming language
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 (−λ i x i )) exp (−μ i y i ) when the searcher and protector allocate resources x i and y i 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