Coalitional multinomial probabilistic values

•These coalitional values take into account players’ attitudes to form coalitions.•We axiomatically characterize these values.•They combine the Shapley value and the multinomial probabilistic values.•They generalize the symmetric coalitional binomial value with no loss of properties.•We give a computational procedure in terms of the multilinear extension of the game.

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 generalizing the symmetric coalitional binomial semivalues. Besides an axiomatic characterization, a computational procedure is provided in terms of the multilinear extension of the game and an application to the Catalonia Parliament, Legislature 2003–2007, is shown.