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From coin tossing to rock-paper-scissors and beyond: a log-exp gap theorem for selecting a leader

Part of: Limit theorems Algorithms - Computer Science Combinatorics

Published online by Cambridge University Press:  04 April 2017

Michael Fuchs ,
Hsien-Kuei Hwang  and
Yoshiaki Itoh
Michael Fuchs*
Affiliation:
National Chiao Tung University
Hsien-Kuei Hwang*
Affiliation:
Academia Sinica
Yoshiaki Itoh*
Affiliation:
Institute of Statistical Mathematics
*
* Postal address: Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 300, Taiwan. Email address: [email protected]
** Postal address: Institute of Statistical Science, Academia Sinica, Taipei, 115, Taiwan.
*** Postal address: Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo, 190-8562, Japan.
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Abstract

A class of games for finding a leader among a group of candidates is studied in detail. This class covers games based on coin tossing and rock-paper-scissors as special cases and its complexity exhibits similar stochastic behaviors: either of logarithmic mean and bounded variance or of exponential mean and exponential variance. Many applications are also discussed.

Keywords

Leader selectionJanken gamerecurrence relationfunctional equationMellin transformsaddle-point methodlimit theoremperiodic functiongap theoremtie

MSC classification

Primary: 60F05: Central limit and other weak theorems 68W40: Analysis of algorithms
Secondary: 05A16: Asymptotic enumeration
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 1 , March 2017 , pp. 213 - 235
Copyright
Copyright © Applied Probability Trust 2017 

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