Skip to main content
Article thumbnail
Location of Repository

On ruckle's conjecture on accumulation games

By Steven Alpern, Robbert Fokkink and Ken Kikuta

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

Topics: QA Mathematics
Publisher: Society for Industrial and Applied Mathematics
Year: 2010
DOI identifier: 10.1137/080741926
OAI identifier: oai:eprints.lse.ac.uk:33599
Provided by: LSE Research Online
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://www.siam.org/journals/s... (external link)
  • http://eprints.lse.ac.uk/33599... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.