Weighted games without a unique minimal representation in integers
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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
Description
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.
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