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k-Balanced games and capacities

Miranda Menéndez, Pedro and Grabisch, Michel (2010) k-Balanced games and capacities. European journal of operational research, 200 (2). pp. 465-472. ISSN 0377-2217

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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 the game. Based on the concept of k-additivity, we define the 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.

Item Type:Article
Uncontrolled Keywords:Cooperative games; k-Additivity; Balanced games; Capacities; Core
Subjects:Sciences > Mathematics > Operations research
ID Code:16939
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Deposited On:31 Oct 2012 09:35
Last Modified:07 Feb 2014 09:38

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