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

Michel Grabisch and Tong Li

European Journal of Operational Research, 2011, vol. 214, issue 3, 697-702

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 [greater-or-equal, slanted] 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.

Keywords: Game; theory; Core; k-Additive; game; Selectope (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (19)

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Working Paper: On the set of imputations induced by the k-additive core (2011)
Working Paper: On the set of imputations induced by the k-additive core (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:214:y:2011:i:3:p:697-702

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