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On the complexity of problems on simple games
(2011-10)
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Simple games cover voting systems in which a single alter-
native, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which ...
Power and potential maps induced by any semivalue: some algebraic properties and computation by multilinear extensions
(Elsevier, 2011-05-16)
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The notions of total power and potential, both defined for any semivalue, give rise to two endomorphisms of the vector space of cooperative games on any given player set where the semivalue is defined. Several properties ...
A note on decisive symmetric games
(2011)
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Binary voting systems, usually represented by simple games, constitute a main DSS topic. A crucial feature of
such a system is the easiness with which a proposal can be collectively accepted, which is measured by ...
Pure bargaining problems and the Shapley rule
(2011)
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Pure bargaining problems with transferable utility are considered. By associating a quasi-additive cooperative game with each one of them, a Shapley rule for this class of problems is derived from the Shapley value for ...
Symmetric coalitional binomial semivalues
(2011-03-01)
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Article.
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We introduce here a family of mixed coalitional values. They extend the binomial semivalues to games endowed with a coalition structure, satisfy the property of symmetry in the quotient game and the quotient game property, ...
The proportional coalitional Shapley value
(2011-06)
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We propose a modification of the Shapley value for monotonic games with a coalition structure. The resulting coalitional value is a twofold extension of the Shapley value in the following sense: (1) the amount obtained by ...