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

Listed author(s):
  • Grabisch, Michel
  • Li, Tong

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.

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Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 214 (2011)
Issue (Month): 3 (November)
Pages: 697-702

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Handle: RePEc:eee:ejores:v:214:y:2011:i:3:p:697-702
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References listed on IDEAS
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  1. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," Annals of Operations Research, Springer, vol. 204(1), pages 33-64, April.
  2. Miranda, Pedro & Grabisch, Michel, 2010. "k-Balanced games and capacities," European Journal of Operational Research, Elsevier, vol. 200(2), pages 465-472, January.
  3. 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.
  4. repec:hal:journl:halshs-00445073 is not listed on IDEAS
  5. 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.
  6. repec:hal:journl:hal-00321625 is not listed on IDEAS
  7. 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.
  8. 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.
  9. 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.
  10. 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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