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

Listed author(s):
  • Michel Grabisch


    (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Tong Li

    (BIT - Beijing Institute of Technology - BIT - Beijing Institute of Technology)

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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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number hal-00625339.

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Date of creation: 2011
Publication status: Published in European Journal of Operational Research, Elsevier, 2011, pp.697-702
Handle: RePEc:hal:cesptp:hal-00625339
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  1. Miranda, Pedro & Grabisch, Michel, 2010. "k-Balanced games and capacities," European Journal of Operational Research, Elsevier, vol. 200(2), pages 465-472, January.
  2. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," Annals of Operations Research, Springer, vol. 204(1), pages 33-64, April.
  3. repec:hal:journl:hal-00321625 is not listed on IDEAS
  4. Michel Grabisch & Pedro Miranda, 2008. "On the vertices of the k-additive core," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00321625, HAL.
  5. Pulido, Manuel A. & Sanchez-Soriano, Joaquin, 2006. "Characterization of the core in games with restricted cooperation," European Journal of Operational Research, Elsevier, vol. 175(2), pages 860-869, December.
  6. Estevez-Fernandez, Arantza & Borm, Peter & Hamers, Herbert, 2006. "On the core of multiple longest traveling salesman games," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1816-1827, November.
  7. repec:hal:journl:halshs-00445073 is not listed on IDEAS
  8. Chateauneuf, Alain & Jaffray, Jean-Yves, 1989. "Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 263-283, June.
  9. Hinojosa, M. A. & Marmol, A. M. & Thomas, L. C., 2005. "Core, least core and nucleolus for multiple scenario cooperative games," European Journal of Operational Research, Elsevier, vol. 164(1), pages 225-238, July.
  10. Jean Derks & Hans Haller & Hans Peters, 2000. "The selectope for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 23-38.
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