# On the set of imputations induced by the k-additive core

Abstract : An extension to the classical notion of core is the notion of $k$-additive core, that is, the set of $k$-additive games which dominate a given game, where a $k$-additive game has its Möbius transform (or Harsanyi dividends) vanishing for subsets of more than $k$ elements. Therefore, the 1-additive core coincides with the classical core. The advantages of the $k$-additive core is that it is never empty once $k\geq 2$, and that it preserves the idea of coalitional rationality. However, it produces $k$-imputations, that is, imputations on individuals and coalitions of at most $k$ individuals, instead of a classical imputation. Therefore one needs to derive a classical imputation from a $k$-order imputation by a so-called sharing rule. The paper investigates what set of imputations the $k$-additive core can produce from a given sharing rule.
Type de document :
Article dans une revue
European Journal of Operational Research, Elsevier, 2011, pp.697-702
Domaine :
Liste complète des métadonnées

Littérature citée [21 références]

https://hal.archives-ouvertes.fr/hal-00625339
Contributeur : Michel Grabisch <>
Soumis le : jeudi 22 septembre 2011 - 17:14:37
Dernière modification le : mardi 27 mars 2018 - 11:48:05
Document(s) archivé(s) le : vendredi 23 décembre 2011 - 02:30:45

### Fichier

ejor10.pdf
Fichiers produits par l'(les) auteur(s)

### Identifiants

• HAL Id : hal-00625339, version 2

### Citation

Michel Grabisch, Tong Li. On the set of imputations induced by the k-additive core. European Journal of Operational Research, Elsevier, 2011, pp.697-702. 〈hal-00625339v2〉

### Métriques

Consultations de la notice

## 361

Téléchargements de fichiers