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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.