Stable Sets in Matching Problems with Coalitional Sovereignty and Path Dominance

17 Pages Posted: 10 Jun 2016

See all articles by P. Jean-Jacques Herings

P. Jean-Jacques Herings

Maastricht University

Ana Mauleon

Université Saint-Louis - Bruxelles; Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE)

Vincent Vannetelbosch

Catholic University of Louvain (UCL)

Date Written: April 20, 2016

Abstract

We study von Neumann Morgenstern stable sets for one-to-one matching problems under the assumption of coalitional sovereignty, meaning that a deviating coalition of players does not have the power to arrange the matches of agents outside the coalition. We study both the case of pairwise and coalitional deviations. We argue further that dominance has to be replaced by path dominance along the lines of van Deemen (1991) and Page and Wooders (2009). This results in the pairwise myopic vNM set and the myopic vNM set, respectively. We obtain a unique prediction for both types of stable sets: the set of matchings that belong to the core. We also show that the pairwise and coalitional analogues of the level-1 farsighted set yield the core as the unique prediction.

Keywords: Matching problems, stable sets, coalitional sovereignty

JEL Classification: C70, C78

Suggested Citation

Herings, P. Jean-Jacques and Mauleon Echeverria, Ana Carmen and Vannetelbosch, Vincent, Stable Sets in Matching Problems with Coalitional Sovereignty and Path Dominance (April 20, 2016). Available at SSRN: https://ssrn.com/abstract=2791994 or http://dx.doi.org/10.2139/ssrn.2791994

P. Jean-Jacques Herings (Contact Author)

Maastricht University ( email )

Department of Economics
P.O. Box 616
6200 MD Maastricht
Netherlands
+31 43 3883636 (Phone)
+31 43 3884878 (Fax)

HOME PAGE: http://www.personeel.unimaas.nl/p.herings/herings.htm

Ana Carmen Mauleon Echeverria

Université Saint-Louis - Bruxelles ( email )

Brussels, 1000
Belgium

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE) ( email )

34 Voie du Roman Pays
B-1348 Louvain-la-Neuve, b-1348
Belgium

Vincent Vannetelbosch

Catholic University of Louvain (UCL) ( email )

CORE, Voie du Roman Pays 34
Louvain-la-Neuve, 1348
Belgium

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