K-balanced games and capacities

Pedro Miranda () and Michel Grabisch
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Pedro Miranda: UCM - Universidad Complutense de Madrid = Complutense University of Madrid [Madrid]

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

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: Coopertaive games; k-additivity; balanced games; capacities; core.; core; jeu coopératif; jeu k-additif; jeu balancé; coeur. (search for similar items in EconPapers)
Date: 2008-11
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00344809v1
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Published in 2008

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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:hal:cesptp:halshs-00344809

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