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Network search games with immobile hider, without a designated searcher starting point

Network search games with immobile hider, without a designated searcher starting point In the (zero-sum) search game Γ(G, x) proposed by Isaacs, the Hider picks a point H in the network G and the Searcher picks a unit speed path S(t) in G with S(0) = x. The payoff to the maximizing Hider is the time T = T(S, H) = min{t : S(t) = H} required for the Searcher to find the Hider. An extensive theory of such games has been developed in the literature. This paper considers the related games Γ(G), where the requirement S(0) = x is dropped, and the Searcher is allowed to choose his starting point. This game has been solved by Dagan and Gal for the important case where G is a tree, and by Alpern for trees with Eulerian networks attached. Here, we extend those results to a wider class of networks, employing theory initiated by Reijnierse and Potters and completed by Gal, for the fixed-start games Γ(G, x). Our results may be more easily interpreted as determining the best worst-case method of searching a network from an arbitrary starting point. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Game Theory Springer Journals

Network search games with immobile hider, without a designated searcher starting point

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References (34)

Publisher
Springer Journals
Copyright
Copyright © 2008 by Springer-Verlag
Subject
Economics; Economic Theory/Quantitative Economics/Mathematical Methods; Game Theory, Economics, Social and Behav. Sciences; Behavioral/Experimental Economics; Operation Research/Decision Theory
ISSN
0020-7276
eISSN
1432-1270
DOI
10.1007/s00182-008-0116-7
Publisher site
See Article on Publisher Site

Abstract

In the (zero-sum) search game Γ(G, x) proposed by Isaacs, the Hider picks a point H in the network G and the Searcher picks a unit speed path S(t) in G with S(0) = x. The payoff to the maximizing Hider is the time T = T(S, H) = min{t : S(t) = H} required for the Searcher to find the Hider. An extensive theory of such games has been developed in the literature. This paper considers the related games Γ(G), where the requirement S(0) = x is dropped, and the Searcher is allowed to choose his starting point. This game has been solved by Dagan and Gal for the important case where G is a tree, and by Alpern for trees with Eulerian networks attached. Here, we extend those results to a wider class of networks, employing theory initiated by Reijnierse and Potters and completed by Gal, for the fixed-start games Γ(G, x). Our results may be more easily interpreted as determining the best worst-case method of searching a network from an arbitrary starting point.

Journal

International Journal of Game Theory – Springer Journals

Published: Feb 13, 2008

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