Weighted games without a unique minimal representation in integers

Freixas Bosch, Josep; Molinero Albareda, Xavier

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Freixas Bosch, Josep

Molinero Albareda, Xavier

Document typeResearch report

Defense date2009

Rights accessRestricted access - author's decision

Abstract

Recerca de jocs amb mínim número de jugadors sense representacions enteres mínimes o mínimes normalitzades

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Isbell in 1959 was the first to find a weighted game without a minimum integer realization in which the affected players do not play a symmetric role in the game. His example has 12 players is a weighted decisive game, i.e. a weighted game for which a coalition wins iff its complement loses. The goal of this paper is to provide a procedure for weighted games that allows finding out what is the minimum number of players needed to get a weighted game without a minimum integer weighted representation in which the affected players do not play a symmetric role in the game. We prove, by means of an algorithm, that the minimum number of voters required is 9.

URIhttp://hdl.handle.net/2117/9295

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Weighted games without a unique minimal representation in integers

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