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A search game with one object and two searchers

Published online by Cambridge University Press:  14 July 2016

Teruhisa Nakai
Teruhisa Nakai*
Affiliation:
Osaka University
*
∗ Postal address: Department of Applied Mathematics, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan.
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Abstract

We consider a non-zero-sum game in which two searchers (player I and II) compete with each other for quicker detection of an object hidden in one of n boxes. Let p (q) be the prior location distribution of the object for player I (II). Exponential detection functions are assumed for both players. Each player wishes to maximize the probability that he detects the object before the opponent detects it. In the general case, a Nash equilibrium point is obtained in the form of a solution of simultaneous differential equations. In the case of p = q, we obtain an explicit solution showing the surprising result that both players have the same equilibrium strategy even though the detection rates are different.

Keywords

SEARCH THEORYTWO-PERSON NON-ZERO-SUM GAMEEXPONENTIAL DETECTION FUNCTIONS

Information

Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 3 , September 1986, pp. 696 - 707
Copyright
Copyright © Applied Probability Trust 1986 

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