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K-balanced games and capacities

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  • Pedro Miranda

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

  • Michel Grabisch

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

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00344809.

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Date of creation: Nov 2008
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Handle: RePEc:hal:cesptp:halshs-00344809

Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00344809
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Related research

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

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Cited by:
  1. Michel Grabisch & Tong Li, 2011. "On the set of imputations induced by the k-additive core," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00625339, 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:journl:halshs-00718358 is not listed on IDEAS

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