Preserving coalitional rationality for non-balanced games
AbstractIn cooperative games, the core is one of the most popular solution concept since it ensures coalitional rationality. For non-balanced games however, the core is empty, and other solution concepts have to be found. We propose the use of general solutions, that is, to distribute the total worth of the game among groups rather than among individuals. In particular, the k-additive core proposed by Grabisch and Miranda is a general solution preserving coalitional rationality which distributes among coalitions of size at most k, and is never ampty for k ? 2. The extended core of Bejan and Gomez can also be viewed as a general solution, since it implies to give an amount to the grand coalition. The k-additive core being an unbounded set and therefore difficult to use in practice, we propose a subset of it called the minimal bargaining set. The idea is to select elements of the k-additive core minimizing the total amount given to coalitions of size greater than 1. Thus the minimum bargaining set naturally reduces to the core for balanced games. We study this set, giving properties and axiomatizations, as well as its relation to the extended core of Bejan and Gomez. We introduce also the notion of unstable coalition, and show how to find them using the minimum bargaining set. Lastly, we give a method of computing the minimum bargaining set.
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Bibliographic InfoPaper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number 12022.
Length: 27 pages
Date of creation: Apr 2012
Date of revision:
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Cooperative game; core; balancedness; general solution.;
Other versions of this item:
- Stéphane Gonzalez & Michel Grabisch, 2012. "Preserving coalitional rationality for non-balanced games," Documents de travail du Centre d'Economie de la Sorbonne 12022r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Apr 2013.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-05-02 (All new papers)
- NEP-GTH-2012-05-02 (Game Theory)
- NEP-HPE-2012-05-02 (History & Philosophy of Economics)
- NEP-MIC-2012-05-02 (Microeconomics)
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