Une représentation simplifiée des jeux simples complets

Abstract

This work is a report of the work of F. Carreras and J. Freixas which deals with theclass of complete simple games and centers on their structure. Using an extension of Is-bell’s desirability relation to coalitions, different from the normally used, F. Carreras and J. Freixas associate with any complete simple game a lattice of coalition models basedupon the types of indifferent players. F. Carreras and J. Freixas establish the basic properties of a vector with natural components and a matrix with non negative integer entries,both closely related to the lattice, which are also shown to be characteristic invariants ofthe game, in the sense that they determine it uniquely up to isomorphisms.