Preserving coalitional rationality for non-balanced games

Stéphane Gonzalez () and Michel Grabisch

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: In 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.

Keywords: Jeux coopératifs; coeur; solution générale; Cooperative game; core; balancedness; general solution (search for similar items in EconPapers)
Date: 2012-04
New Economics Papers: this item is included in nep-gth, nep-hpe and nep-mic
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00718358v2
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Published in 2012

Downloads: (external link)
https://shs.hal.science/halshs-00718358v2/document (application/pdf)

Related works:
Journal Article: Preserving coalitional rationality for non-balanced games (2015)
Working Paper: Preserving coalitional rationality for non-balanced games (2015)
Working Paper: Preserving coalitional rationality for non-balanced games (2015)
Working Paper: Preserving coalitional rationality for non-balanced games (2015)
Working Paper: Preserving coalitional rationality for non-balanced games (2013)
Working Paper: Preserving coalitional rationality for non-balanced games (2012)
Working Paper: Preserving coalitional rationality for non-balanced games (2012)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:halshs-00718358

Access Statistics for this paper

More papers in Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL
Bibliographic data for series maintained by CCSD ().