Bases and Linear Transforms of Cooperation systems

Abstract : We study linear properties of TU-games, revisiting well-known issues like interaction transforms, the inverse Shapley value problem and potentials. We embed TU-games into the model of cooperation systems and influence patterns, which allows us to introduce linear operators on games in a natural way. We focus on transforms, which are linear invertible maps, relate them to bases and investigate many examples (Möbius transform, interaction transform, Walsh transform and Fourier analysis etc.). In particular, we present a simple solution to the inverse problem in its general form: Given a linear value Φ and a game v, find all games v' such that Φ(v) = Φ(v' ). Generalizing Hart and Mas-Colell's concept of a potential, we introduce general potentials and show that every linear value is induced by an appropriate potential.
Type de document :
Autre publication
Documents de travail du Centre d'Economie de la Sorbonne 2014.10R - ISSN : 1955-611X. 2015
Liste complète des métadonnées

Littérature citée [24 références]  Voir  Masquer  Télécharger

https://halshs.archives-ouvertes.fr/halshs-00971393
Contributeur : Lucie Label <>
Soumis le : mercredi 10 juin 2015 - 16:16:40
Dernière modification le : mardi 27 mars 2018 - 11:48:05
Document(s) archivé(s) le : mardi 25 avril 2017 - 06:31:57

Fichier

14010R.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : halshs-00971393, version 2

Collections

Citation

Ulrich Faigle, Michel Grabisch. Bases and Linear Transforms of Cooperation systems. Documents de travail du Centre d'Economie de la Sorbonne 2014.10R - ISSN : 1955-611X. 2015. 〈halshs-00971393v2〉

Partager

Métriques

Consultations de la notice

262

Téléchargements de fichiers

396