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

Michel Grabisch and Tong Li
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Tong Li: BIT - Beijing Institute of Technology

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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.

Date: 2011
Note: View the original document on HAL open archive server: https://hal.science/hal-00625339v2
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Citations: View citations in EconPapers (19)

Published in European Journal of Operational Research, 2011, pp.697-702

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Journal Article: 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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