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Von Neumann-Morgenstern stable sets in matching problems

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  • Ehlers, Lars

Abstract

The following properties of the core of a one-to-one matching problem are well-known: (i) the core is non-empty; (ii) the core is a lattice; and (iii) the set of unmatched agents is identical for any two matchings belonging to the core. The literature on two-sided matching focuses almost exclusively on the core and studies extensively its properties. Our main result is the following characterization of (von Neumann-Morgenstern) stable sets in one-to-one matching problems. We show that a set of matchings is a stable set of a one-to-one matching problem only if it is a maximal set satisfying the following properties: (a) the core is a subset of the set; (b) the set is a lattice; and (c) the set of unmatched agents is identical for any two matchings belonging to the set. Furthermore, a set is a stable set if it is the unique maximal set satisfying properties (a), (b), and (c). We also show that our main result does not extend from one-to-one matching problems to many-to-one matching problems.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 134 (2007)
Issue (Month): 1 (May)
Pages: 537-547

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Handle: RePEc:eee:jetheo:v:134:y:2007:i:1:p:537-547

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Web page: http://www.elsevier.com/locate/inca/622869

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  1. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
  2. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer, vol. 15(3), pages 187-200.
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Cited by:
  1. Otto, Philipp E. & Bolle, Friedel, 2009. "Small numbers matching markets: Unstable and inefficient due to over-competition?," Discussion Papers 270, European University Viadrina Frankfurt (Oder), Department of Business Administration and Economics.
  2. Bettina Klaus & Flip Klijn & Markus Walzl, 2009. "Farsighted Stability for Roommate Markets," Working Papers 385, Barcelona Graduate School of Economics.
  3. Florian M. Biermann, 2011. "A Measure to compare Matchings in Marriage Markets," Discussion Paper Series dp575, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  4. Ana, MAULEON & Vincent, VANNETELBOSCH & Wouter, VERGOTE, 2008. "Von Neuman-Morgenstern farsightedly stable sets in two-sided matching," Discussion Papers (ECON - Département des Sciences Economiques) 2008013, Université catholique de Louvain, Département des Sciences Economiques.
  5. Luo, Xiao, 2009. "The foundation of stability in extensive games with perfect information," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 860-868, December.
  6. Philipp Otto & Friedel Bolle, 2011. "Matching markets with price bargaining," Experimental Economics, Springer, vol. 14(3), pages 322-348, September.
  7. Weese, Eric, 2013. "Political Mergers as Coalition Formation: An Analysis of the Heisei Municipal Amalgamations," Working Papers 113, Yale University, Department of Economics.
  8. MAULEON, Ana & MOLIS, Elena & VANNETELBOSCH, Vincent & VERGOTE, Wouter, 2011. "Absolutely stable roommate problems," CORE Discussion Papers 2011029, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Dinko Dimitrov & Shao Chin Sung, 2011. "Size Monotonicity and Stability of the Core in Hedonic Games," Working Papers 2011.52, Fondazione Eni Enrico Mattei.
  10. Núñez, Marina & Rafels, Carles, 2013. "Von Neumann–Morgenstern solutions in the assignment market," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1282-1291.
  11. Larrea Jaurrieta, María Concepción & Iñarra García, María Elena & Molis Bañales, Elena, 2007. "The Stability of the Roommate Problem Revisited," IKERLANAK 2007-30, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
  12. Iñarra, E. & Larrea, C. & Molis, E., 2013. "Absorbing sets in roommate problems," Games and Economic Behavior, Elsevier, vol. 81(C), pages 165-178.
  13. Eric Weese, 2013. "Political Mergers as Coalition Formation: An Analysis of the Heisei Municipal Amalgamations," Working Papers 1022, Economic Growth Center, Yale University.
  14. Marina Núñez & Carles Rafels, 2009. "Von Neumann–Morgenstern stable-set solutions in the assignment market," Working Papers 412, Barcelona Graduate School of Economics.
  15. Toshiyuki Hirai, 2008. "von Neumann–Morgenstern stable sets of income tax rates in public good economies," Economic Theory, Springer, vol. 37(1), pages 81-98, October.
  16. MAULEON, Ana & MOLIS, Elena & VANNETELBOSCH, Vincent & VERGOTE , Wouter, 2013. "Dominance invariant one-to-one matching problems," CORE Discussion Papers 2013052, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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