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The three colour hat guessing game on cycle graphs

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dc.abstract.enWe study a cooperative game in which each member of a team of N players, wearing coloured hats and situated at the vertices of the cycle graph with N vertices, is guessing their own hat colour merely on the basis of observing the hats worn by their two neighbours without exchanging the information. Each hat can have one of three colours. A predetermined guessing strategy is winning if it guarantees at least one correct individual guess for every assignment of colours. We prove that a winning strategy exists if and only if N is divisible by 3 or N = 4. This asymmetric game is an example of relational system using incomplete information about an unpredictable situation, where at least one participant has to act properly.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorSzczechla, Witold
dc.date.accessioned2024-01-26T10:49:33Z
dc.date.available2024-01-26T10:49:33Z
dc.date.issued2017
dc.description.financeNie dotyczy
dc.description.number1 #P1.37
dc.description.volume24
dc.identifier.issn1097-1440
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/123226
dc.identifier.weblinkhttp://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i1p37/pdf
dc.languageeng
dc.relation.ispartofElectronic Journal of Combinatorics
dc.relation.pages1-19
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.subject.enCooperative games
dc.subject.enGames on graphs
dc.subject.enHat puzzle
dc.subject.enHat guessing problems
dc.subject.enDeterministic strategy
dc.subject.enSystem reliability
dc.subject.enInformation network
dc.subject.enGraph colouring
dc.titleThe three colour hat guessing game on cycle graphs
dc.typeJournalArticle
dspace.entity.typePublication