Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-06-02T00:39:31.931Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Corwin, T. L. (1981) Search for a moving target under minimax estimation. J. Appl. Prob. 18, 167–180.Google Scholar
[2] Croucher, J. S. (1975) Application of the fundamental theorem of games to an example concerning antiballistic missile defense. Naval Res. Logist. Quart. 22, 197–203.CrossRefGoogle Scholar
[3] Gal, S. (1978) A stochastic search game. SIAM J. Appl. Math. 34, 205–210.Google Scholar
[4] Gittins, J. C. and Roberts, D. M. (1979) The search for an intelligent evader concealed in one of an arbitrary number of regions. Naval Res. Logist. Quart. 26, 651–666.Google Scholar
[5] Lee, K. T. (1983) A firing game with time lag. J. Optim. Theory Appl. 41, 547–558.Google Scholar
[6] Nakai, T. (1983) A sequential evasion-search game. Math. Japonica 28, 315–326.Google Scholar
[7] Nakai, T. (1984) A sequential evasion-search game with a goal. Unpublished.Google Scholar
[8] Nash, J. F. (1951) Non-cooperative games. Ann. Math. 54, 286–295.Google Scholar
[9] Neuts, M. F. (1963) A multistage search game. J. SIAM 11, 502–507.Google Scholar
[10] Norris, R. C. (1962) Studies in search for a conscious evader. MIT Lincoln Lab. Tech. Rpt. No. 279.Google Scholar
[11] Roberts, D. M. and Gittins, J. C. (1978) The search for an intelligent evader: strategies for searcher and evader in the two-region problem. Naval Res. Logist. Quart. 25, 95–106.Google Scholar
[12] Ruckle, W. H. (1979) On the constructability of solution to a pair of two person search games. Int. J. Game Theory 8, 235–240.Google Scholar
[13] Ruckle, W. H. (1981) Pursuit on a cyclic graph — the symmetric stochastic case. Int. J. Game Theory 10, 91–99.CrossRefGoogle Scholar
[14] Sakaguchi, M. (1973) Two-sided search games. J. Operat. Res. Soc. Japan 16, 207–225.Google Scholar
[15] Stewart, T. J. (1981) A two-cell model of search for an evading target. European J. Operat. Res. 8, 369–378.Google Scholar
[16] Suberman, E. J. (1981) A hide-search game. J. Appl. Prob. 18, 628–640.Google Scholar
[17] Washburn, A. R. (1980) Search-evasion game in a fixed region. Operat. Res. 28, 1290–1298.CrossRefGoogle Scholar