We introduce a new family of coalitional values designed to take into account players’ attitudes with regard to cooperation. This new family of values applies to cooperative games with a coalition structure by combining the Shapley value and the multinomial probabilistic values, thus...

Partnership formation in cooperative games is studied, and binomial semivalues are used to measure the effects of such a type of coalition arising from an agreement between (a group of) players. The joint effect on the set of involved players is also compared with that of the alternative...

Gvozdeva et al. (Int J Game Theory, doi:<ExternalRef> <RefSource>10.1007/s00182-011-0308-4</RefSource> <RefTarget Address="10.1007/s00182-011-0308-4" TargetType="DOI"/> </ExternalRef>, <CitationRef CitationID="CR17">2013</CitationRef>) have introduced three hierarchies for simple games in order to measure the distance of a given simple game to the class of (roughly) weighted voting games. Their third class <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$${\mathcal {C}}_\alpha $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi mathvariant="script">C</mi> <mi mathvariant="italic">α</mi> </msub> </math> </EquationSource> </InlineEquation>...</equationsource></equationsource></inlineequation></citationref></refsource></externalref>

Tomiyama [Tomiyama, Y., 1987. Simple game, voting representation and ordinal power equivalence. International Journal on Policy and Information 11, 67-75] proved that, for every weighted majority game, the preorderings induced by the classical Shapley-Shubik and Penrose-Banzhaf-Coleman indices...