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

  • Michel Grabisch

    ()

    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

  • Tong Li

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

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
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Publication status: Published, European Journal of Operational Research, 2011, 697-702
Handle: RePEc:hal:cesptp:hal-00625339
Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00625339
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  1. 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.
  2. 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.
  3. Miranda, Pedro & Grabisch, Michel, 2010. "k-Balanced games and capacities," European Journal of Operational Research, Elsevier, vol. 200(2), pages 465-472, January.
  4. Michel Grabisch, 2009. "The core of games on ordered structures and graphs," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445171, HAL.
  5. Jean Derks & Hans Haller & Hans Peters, 2000. "The selectope for cooperative games," International Journal of Game Theory, Springer, vol. 29(1), pages 23-38.
  6. Estevez Fernandez, M.A. & Borm, P.E.M. & Hamers, H.J.M., 2003. "On the Core of Multiple Longest Traveling Salesman Games," Discussion Paper 2003-127, Tilburg University, Center for Economic Research.
  7. Pedro Miranda & Michel Grabisch, 2010. "k-balanced games and capacities," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445073, HAL.
  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. 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.
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