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Summary: Coin-flipping games immune against linear-sized coalitions
Noga Alon
Tel Aviv University
Moni Naor
IBM Almaden Research Center
February 22, 2002
Abstract
Perfect information coin-flipping and leader-election games arise naturally in the study of
fault tolerant distributed computing and have been considered in many different scenarios.
Answering a question of Ben-Or and Linial we prove that for every c < 1 there are such games
on n players in which no coalition of cn players can influence the outcome with probability
greater than some universal constant times c. (Note that we actually prove this statement only
for all c < 1/3, but since our universal constant is bigger than 3 the above is trivial for c 1/3.)
We show that a random protocol of a certain length has this property and give an explicit
construction as well.
Address: Eskenazy School of Mathematics, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv,
Israel. e-mail: noga@taurus.bitnet. Most of this work was done while the author was visiting IBM Almaden Research
Center.
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