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On ruckle's conjecture on accumulation games

Alpern, Steven, Fokkink, Robbert and Kikuta, Ken (2010) On ruckle's conjecture on accumulation games. SIAM Journal on Control and Optimization, 48 (8). pp. 5073-5083. ISSN 0363-0129

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Abstract

In an accumulation game, the Hider secretly distributes his given total wealth h among n locations, while the Searcher picks r locations and confiscates the material placed there. The Hider wins if what is left at the remaining n - r locations is at least 1; otherwise the Searcher wins. Ruckle's conjecture says that an optimal Hider strategy is to put an equal amount h/k at k randomly chosen locations for some k. We extend the work of Kikuta and Ruckle by proving the conjecture for several cases, e.g., r = 2 or n - 2; n ≤ 7; n = 2r - 1; h ≤ 2 + 1/ (n - r)and n ≤ 2r.The last result uses the Erdo″s-Ko-Rado theorem. We establish a con nection between Ruckle's conjecture and the Hoeffding problem of bounding tail probabilities of sums of random variables.

Item Type: Article
Official URL: http://www.siam.org/journals/sicon.php
Additional Information: © 2010 Society for Industrial and Applied Mathematics
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 30 Mar 2011 11:58
URL: http://eprints.lse.ac.uk/33599/

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