NDLI: New Constructions and Bounds for Winkler's Hat Game

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Georgiou, Nicholas Gadouleau, Maximilien
Copyright Year	2015
Abstract	Hat problems have recently become a popular topic in combinatorics and discrete mathematics. These have been shown to be strongly related to coding theory, network coding, and auctions. We consider the following version of the hat game, introduced by Winkler and studied by Butler et al. A team is composed of several players; each player is assigned a hat of a given color; they do not see their own color but can see some other hats, according to a directed graph. The team wins if they have a strategy such that, for any possible assignment of colors to their hats, at least one player guesses their own hat color correctly. In this paper, we discover some new classes of graphs which allow a winning strategy, thus answering some of the open questions of Butler et al. We also derive upper bounds on the maximal number of possible hat colors that allow for a winning strategy for a given graph.
Starting Page	823
Ending Page	834
Page Count	12
File Format	PDF
ISSN	08954801
DOI	10.1137/130944680
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	2
Volume Number	29
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2015-04-21
Access Restriction	Subscribed
Subject Keyword	deterministic strategies directed graphs Directed graphs (digraphs), tournaments hat game Cooperative games
Content Type	Text
Resource Type	Article
Subject	Mathematics

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