Symmetric coalitional binomial semivalues

Abstract

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 quotidient game and the quotient game property, generalize the symmetric coalitional Banzhaf value introduced by Alonso and Fiestras and link and merge the shapley value and the binomial semivalues. A computational procedure in terms of the multilinear extension of the original game is also provided and an application to political science is sketched.