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The solution to an open problem for a caching game

Csóka, Endre and Lidbetter, Thomas (2016) The solution to an open problem for a caching game. Naval Research Logistics, 63 (1). pp. 23-31. ISSN 0894-069X

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Identification Number: 10.1002/nav.21674

Abstract

In a caching game introduced by Alpern et al. [3], a Hider who can dig to a total fixed depth normalized to 1 buries a fixed number of objects among n discrete locations. A Searcher who can dig to a total depth of h searches the locations with the aim of finding all of the hidden objects. If he does so, he wins, otherwise the Hider wins. This zero-sum game is complicated to analyze even for small values of its parameters, and for the case of 2 hidden objects has been completely solved only when the game is played in up to 3 locations. For some values of h the solution of the game with 2 objects hidden in 4 locations is known, but the solution in the remaining cases was an open question recently highlighted by Fokkink et al. [13]. Here we solve the remaining cases of the game with 2 objects hidden in 4 locations. We also give some more general results for the game, in particular using a geometrical argument to show that when there are 2 objects hidden in n locations and n ! 1, the value of the game is asymptotically equal to h=n for h � n=2.

Item Type: Article
Official URL: http://onlinelibrary.wiley.com/journal/10.1002/(IS...
Additional Information: © 2015 Wiley Periodicals, Inc.
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 16 Dec 2015 11:36
Last Modified: 20 Feb 2019 11:36
Projects: 306493, 648017
Funders: European Research Council
URI: http://eprints.lse.ac.uk/id/eprint/64724

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