K-balanced games and capacities

Pedro Miranda () and Michel Grabisch
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Pedro Miranda: Department of Statistics and O.R. - Universidad Complutense de Madrid

Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), 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

Keywords: Cooperative games; k-additivity; balanced games; capacities; core (search for similar items in EconPapers)
JEL-codes: C7 D7 (search for similar items in EconPapers)
Pages: 26 pages
Date: 2008-11
New Economics Papers: this item is included in nep-gth
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ftp://mse.univ-paris1.fr/pub/mse/CES2008/B08079.pdf (application/pdf)

Related works:
Journal Article: k-Balanced games and capacities (2010)
Working Paper: k-balanced games and capacities (2010)
Working Paper: k-balanced games and capacities (2010)
Working Paper: K-balanced games and capacities (2008)
Working Paper: K-balanced games and capacities (2008)
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Persistent link: https://EconPapers.repec.org/RePEc:mse:cesdoc:b08079

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