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
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.
|Additional Information:||© 2010 Society for Industrial and Applied Mathematics|
|Uncontrolled Keywords:||accumulation game, intersecting families, optimal strategies, sums of random variables, tail probability|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
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