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K-balanced games and capacities

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Author Info

  • Pedro Miranda

    ()
    (Department of Statistics and O.R. - Universidad Complutense de Madrid)

  • Michel Grabisch

    ()
    (Centre d'Economie de la Sorbonne)

Abstract

In this paper, we present a generalization of the concept of balanced game for finite games. Balanced games are those having a nonempty core, and this core is usually considered as the solution of game. Based on the concept of k-additivity, we define to so-called k-balanced games and the corresponding generalization of core, the k-additive core, whose elements are not directly imputations but k-additive games. We show that any game is k-balanced for a suitable choice of k, so that the corresponding k-additive core is not empty. For the games in the k-additive core, we propose a sharing procedure to get an imputation and a representative value for the expectations of the players based on the pessimistic criterion. Moreover, we look for necessary and sufficient conditions for a game to be k-balanced. For the general case, it is shown that any game is either balanced or 2-balanced. Finally, we treat the special case of capacities.

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File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2008/B08079.pdf
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Bibliographic Info

Paper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number b08079.

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Length: 26 pages
Date of creation: Nov 2008
Date of revision:
Handle: RePEc:mse:cesdoc:b08079

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Related research

Keywords: Cooperative games; k-additivity; balanced games; capacities; core.;

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Cited by:
  1. Stéphane Gonzalez & Michel Grabisch, 2012. "Preserving coalitional rationality for non-balanced games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00718358, HAL.
  2. Stéphane Gonzalez & Michel Grabisch, 2012. "Preserving coalitional rationality for non-balanced games," Documents de travail du Centre d'Economie de la Sorbonne 12022r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Apr 2013.
  3. repec:hal:cesptp:hal-00625339 is not listed on IDEAS
  4. repec:hal:journl:halshs-00718358 is not listed on IDEAS
  5. Grabisch, Michel & Li, Tong, 2011. "On the set of imputations induced by the k-additive core," European Journal of Operational Research, Elsevier, vol. 214(3), pages 697-702, November.

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