k-balanced games and capacities
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.
|Date of creation:||Jan 2010|
|Publication status:||Published in European Journal of Operational Research, Elsevier, 2010, 200 (2), pp.465-472. 〈10.1016/j.ejor.2008.12.020〉|
|Note:||View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00445073|
|Contact details of provider:|| Web page: https://hal.archives-ouvertes.fr/|
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- repec:hal:journl:hal-00321625 is not listed on IDEAS
- Michel Grabisch & Pedro Miranda, 2008. "On the vertices of the k-additive core," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00321625, HAL.
- Chateauneuf, Alain & Jaffray, Jean-Yves, 1989.
"Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion,"
Mathematical Social Sciences,
Elsevier, vol. 17(3), pages 263-283, June.
- Alain Chateauneuf & Jean-Yves Jaffray, 2008. "Some Characterizations of Lower Probabilities and Other Monotone Capacities through the Use of Mobius Inversion," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00649208, HAL.
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