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]

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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.

Keywords: Cooperative Games; k-additivity; balanced games; capacities; core (search for similar items in EconPapers)
Date: 2010-01
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00445073
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Citations: View citations in EconPapers (24)

Published in European Journal of Operational Research, 2010, 200 (2), pp.465-472. ⟨10.1016/j.ejor.2008.12.020⟩

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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 (2008)
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:journl:halshs-00445073

DOI: 10.1016/j.ejor.2008.12.020

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