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Stable sets in matching problems with coalitional sovereignty and path dominance |
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| Institution: | 1. Department of Economics, Maastricht University, Maastricht, The Netherlands;2. CEREC, Saint-Louis University, Brussels, Belgium;3. CORE, University of Louvain, Louvain-la-Neuve, Belgium;1. Department of Economics, Universidad Carlos III de Madrid, c/ Madrid 126, 28903 Getafe (Madrid), Spain;1. Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Napoli Federico II, Italy;2. CSEF, Italy;3. School of Applied Mathematics and Physical Sciences, Department of Mathematics, National Technical University of Athens, Greece;1. Department of Economics and Management, Université de Cergy-Pontoise & THEMA,Cergy-Pontoise, 95011, France;2. Department of Economics, University of Georgia, Athens, GA, 30602, USA |
| Abstract: | We study von Neumann Morgenstern stable sets for one-to-one matching problems under the assumption of coalitional sovereignty (C), 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 (P) along the lines of van Deemen (1991) and Page and Wooders (2009). This results in the pairwise CP vNM set in the case of pairwise deviations and the CP vNM set in the case of coalitional deviations. We obtain a unique prediction for both types of stable sets: the set of matchings that belong to the core. |
| Keywords: | Matching problems Stable sets Enforceability Coalitional sovereignty Path dominance |
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