# 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.
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Journal articles
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Cited literature [21 references]

https://hal.archives-ouvertes.fr/hal-00625339
Contributor : Michel Grabisch <>
Submitted on : Thursday, September 22, 2011 - 5:14:37 PM
Last modification on : Tuesday, March 27, 2018 - 11:48:05 AM
Long-term archiving on : Friday, December 23, 2011 - 2:30:45 AM

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• 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⟩

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