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

## 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 |
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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 |

Date Deposited: | 30 Mar 2011 11:58 |

URL: | http://eprints.lse.ac.uk/33599/ |

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