IDEAS home Printed from https://ideas.repec.org/p/huj/dispap/dp501.html
   My bibliography  Save this paper

General Matching: Lattice Structure of the Set of Agreements

Author

Listed:
  • Aron Matskin
  • Daniel Lehmann

Abstract

The subset agreement problem generalizes all forms of two-sided matching. Two agents need to agree on some subset of a given finite set of contracts. A solution concept - agreement - generalizes the notion of a stable subset. Its definition does not require the consideration of a preference ordering on sets of contracts, but only that of the choice function that reveals the agents' preferences by choosing the best subset of any given set of contracts. Under a suitable condition, called coherence, that requires that contracts are substitutes to one another, at least one greement always exists. A constructive proof is given that the structure of the set of agreements is a lattice.

Suggested Citation

  • Aron Matskin & Daniel Lehmann, 2009. "General Matching: Lattice Structure of the Set of Agreements," Discussion Paper Series dp501, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  • Handle: RePEc:huj:dispap:dp501
    as

    Download full text from publisher

    File URL: http://ratio.huji.ac.il/sites/default/files/publications/dp501.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Brewer, Paul J. & Plott, Charles R., 1996. "A binary conflict ascending price (BICAP) mechanism for the decentralized allocation of the right to use railroad tracks," International Journal of Industrial Organization, Elsevier, pages 857-886.
    2. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
    3. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, pages 863-872.
    4. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    5. Alkan, Ahmet & Gale, David, 2003. "Stable schedule matching under revealed preference," Journal of Economic Theory, Elsevier, vol. 112(2), pages 289-306, October.
    6. Brewer, Paul J. & Plott, Charles R., 1996. "A binary conflict ascending price (BICAP) mechanism for the decentralized allocation of the right to use railroad tracks," International Journal of Industrial Organization, Elsevier, pages 857-886.
    7. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    8. Zimmermann, Klaus F, 1996. "Wage and Mobility Effects of Trade and Migration," CEPR Discussion Papers 1318, C.E.P.R. Discussion Papers.
    9. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
    10. Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-1091, November.
    11. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
    12. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
    13. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    14. Alvin E. Roth, 1985. "Conflict and Coincidence of Interest in Job Matching: Some New Results and Open Questions," Mathematics of Operations Research, INFORMS, vol. 10(3), pages 379-389, August.
    15. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
    16. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, pages 913-935.
    17. Michael Ostrovsky, 2008. "Stability in Supply Chain Networks," American Economic Review, American Economic Association, pages 897-923.
    18. Elliott Peranson & Alvin E. Roth, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," American Economic Review, American Economic Association, pages 748-780.
    Full references (including those not matched with items on IDEAS)

    More about this item

    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:huj:dispap:dp501. 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: (Michael Simkin). General contact details of provider: http://edirc.repec.org/data/crihuil.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 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.