Pedro Miranda () (Universidad Complutense de Madrid - Department of Statistics and O.R.) Michel Grabisch () (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I)
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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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Length: Date of creation: Nov 2008 Date of revision: Handle: RePEc:hal:cesptp:halshs-00344809_v1
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