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Article Dans Une Revue European Journal of Operational Research Année : 2011

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

Résumé

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.
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Dates et versions

hal-00625339 , version 1 (21-09-2011)
hal-00625339 , version 2 (22-09-2011)

Identifiants

  • HAL Id : hal-00625339 , version 1

Citer

Michel Grabisch, Li Tong. On the set of imputations induced by the k-additive core. European Journal of Operational Research, 2011, pp.697-702. ⟨hal-00625339v1⟩
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