IDEAS home Printed from https://ideas.repec.org/p/mtl/montec/12-2005.html
   My bibliography  Save this paper

Von Neumann-Morgenstern Stable Sets in Matching Problems

Author

Listed:
  • 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.

Suggested Citation

  • EHLERS, Lars, 2005. "Von Neumann-Morgenstern Stable Sets in Matching Problems," Cahiers de recherche 12-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    • Handle: RePEc:mtl:montec:12-2005
    as

    Download full text from publisher

    File URL: http://www.cireqmontreal.com/wp-content/uploads/cahiers/12-2005-cah.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Klijn, Flip & Masso, Jordi, 2003. "Weak stability and a bargaining set for the marriage model," Games and Economic Behavior, Elsevier, vol. 42(1), pages 91-100, January.
    2. Alkan, Ahmet & Gale, David, 2003. "Stable schedule matching under revealed preference," Journal of Economic Theory, Elsevier, vol. 112(2), pages 289-306, October.
    3. Ahmet Alkan, 2001. "original papers : On preferences over subsets and the lattice structure of stable matchings," Review of Economic Design, Springer;Society for Economic Design, vol. 6(1), pages 99-111.
    4. Biswas, Amit K. & Parthasarathy, T. & Ravindran, G., 2001. "Stability and Largeness of the Core," Games and Economic Behavior, Elsevier, vol. 34(2), pages 227-237, February.
    5. Echenique, Federico & Oviedo, Jorge, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, vol. 1(2), pages 233-273, June.
    6. Echenique, Federico & Oviedo, Jorge, 2004. "Core many-to-one matchings by fixed-point methods," Journal of Economic Theory, Elsevier, vol. 115(2), pages 358-376, April.
    7. Einy, Ezra & Holzman, Ron & Monderer, Dov & Shitovitz, Benyamin, 1996. "Core and Stable Sets of Large Games Arising in Economics," Journal of Economic Theory, Elsevier, vol. 68(1), pages 200-211, January.
    8. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 187-200.
    9. Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
    10. Einy, Ezra & Shitovitz, Benyamin, 2003. "Symmetric von Neumann-Morgenstern stable sets in pure exchange economies," Games and Economic Behavior, Elsevier, vol. 43(1), pages 28-43, April.
    11. Demange, Gabrielle, 1987. "Nonmanipulable Cores," Econometrica, Econometric Society, vol. 55(5), pages 1057-1074, September.
    12. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, January.
    13. Sasaki, Hiroo & Toda, Manabu, 1992. "Consistency and characterization of the core of two-sided matching problems," Journal of Economic Theory, Elsevier, vol. 56(1), pages 218-227, February.
    14. Einy, Ezra & Holzman, Ron & Monderer, Dov & Shitovitz, Benyamin, 1997. "Core Equivalence Theorems for Infinite Convex Games," Journal of Economic Theory, Elsevier, vol. 76(1), pages 1-12, September.
    15. Peleg, Bezalel, 1986. "A proof that the core of an ordinal convex game is a von Neumann-Morgenstern solution," Mathematical Social Sciences, Elsevier, vol. 11(1), pages 83-87, February.
    16. Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2000. "Single Agents and the Set of Many-to-One Stable Matchings," Journal of Economic Theory, Elsevier, vol. 91(1), pages 91-105, March.
    17. Zhou Lin, 1994. "A New Bargaining Set of an N-Person Game and Endogenous Coalition Formation," Games and Economic Behavior, Elsevier, vol. 6(3), pages 512-526, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mauleon, Ana & Vannetelbosch, Vincent J. & Vergote, Wouter, 2011. "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," Theoretical Economics, Econometric Society, vol. 6(3), September.
    2. Eric Weese, 2015. "Political mergers as coalition formation: An analysis of the Heisei municipal amalgamations," Quantitative Economics, Econometric Society, vol. 6(2), pages 257-307, July.
    3. Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
    4. Philipp Otto & Friedel Bolle, 2011. "Matching markets with price bargaining," Experimental Economics, Springer;Economic Science Association, vol. 14(3), pages 322-348, September.
    5. Iñarra García, María Elena & Larrea Jaurrieta, María Concepción & 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.
    6. Jean-Jacques Herings, P. & Mauleon, Ana & Vannetelbosch, Vincent, 2017. "Stable sets in matching problems with coalitional sovereignty and path dominance," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 14-19.
    7. Marina Núñez & Carles Rafels, 2009. "Von Neumann-Morgenstern stable-set solutions in the assignment market," Working Papers 412, Barcelona Graduate School of Economics.
    8. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2017. "Matching with Myopic and Farsighted Players," Research Memorandum 011, Maastricht University, Graduate School of Business and Economics (GSBE).
    9. 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).
    10. Francis Bloch & Anne van den Nouweland, 2017. "Farsighted Stability with Heterogeneous Expectations," Working Papers 2017.31, Fondazione Eni Enrico Mattei.
    11. Florian M. Biermann, 2011. "A Measure to compare Matchings in Marriage Markets," Discussion Paper Series dp575, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    12. Doğan, Battal, 2016. "Responsive affirmative action in school choice," Journal of Economic Theory, Elsevier, vol. 165(C), pages 69-105.
    13. Dinko Dimitrov & Shao Chin Sung, 2011. "Size Monotonicity and Stability of the Core in Hedonic Games," Working Papers 2011.52, Fondazione Eni Enrico Mattei.
    14. Hannu Vartiainen, 2015. "Dynamic stable set as a tournament solution," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(2), pages 309-327, September.
    15. Herings, P.J.J. & Mauleon, A. & Vannetelbosch, V., 2014. "Stability of networks under level-k farsightedness," Research Memorandum 030, Maastricht University, Graduate School of Business and Economics (GSBE).
    16. 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.
    17. Bando, Keisuke, 2014. "On the existence of a strictly strong Nash equilibrium under the student-optimal deferred acceptance algorithm," Games and Economic Behavior, Elsevier, vol. 87(C), pages 269-287.
    18. Bettina Klaus & Flip Klijn & Markus Walzl, 2011. "Farsighted Stability for Roommate Markets," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 13(6), pages 921-933, December.
    19. 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.
    20. Toshiyuki Hirai, 2008. "von Neumann–Morgenstern stable sets of income tax rates in public good economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(1), pages 81-98, October.
    21. Ana Mauleon & Elena Molis & Vincent Vannetelbosch & Wouter Vergote, 2014. "Dominance invariant one-to-one matching problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 925-943, November.
    22. Iñarra, E. & Larrea, C. & Molis, E., 2013. "Absorbing sets in roommate problems," Games and Economic Behavior, Elsevier, vol. 81(C), pages 165-178.
    23. Núñez, Marina & Rafels, Carles, 2013. "Von Neumann–Morgenstern solutions in the assignment market," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1282-1291.

    More about this item

    Keywords

    matching problem; Von Neumann-Morgenstern stable sets;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • J41 - Labor and Demographic Economics - - Particular Labor Markets - - - Labor Contracts
    • J44 - Labor and Demographic Economics - - Particular Labor Markets - - - Professional Labor Markets and Occupations

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mtl:montec:12-2005. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sharon BREWER). General contact details of provider: http://edirc.repec.org/data/cdmtlca.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.