Advanced Search
MyIDEAS: Login to save this paper or follow this series

Credible Group Stability in Many-to-Many Matching Problems

Contents:

Author Info

  • Hideo Konishi

    (Boston College)

  • M. Utku Ünver

    (Koç University)

Abstract

It is known that in two-sided many-to-many matching problems, pairwise stable matchings may not be immune to group deviations, unlike in many- to-one matching problems (Blair 1988). In this paper, we show that pairwise stability is equivalent to credible group stability when one side has responsive preferences and the other side has categorywise- responsive preferences. A credibly group-stable matching is immune to any “executable” group deviations with an appropriate definition of executability. Under the same preference restriction, we also show the equivalence between the set of pairwise-stable matchings and the set of matchings generated by coalition-proof Nash equilibria of an appropriately defined strategic-form game.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://128.118.178.162/eps/game/papers/0309/0309005.pdf
Download Restriction: no

Bibliographic Info

Paper provided by EconWPA in its series Game Theory and Information with number 0309005.

as in new window
Length:
Date of creation: 06 Sep 2003
Date of revision: 06 Sep 2003
Handle: RePEc:wpa:wuwpga:0309005

Contact details of provider:
Web page: http://128.118.178.162

Related research

Keywords:

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
  2. Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 55-70, July.
  3. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, Econometric Society, vol. 50(6), pages 1483-1504, November.
  4. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, Econometric Society, vol. 52(1), pages 47-57, January.
  5. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
  6. Effrosyni Diamantoudi & Eiichi Miyagawa & Licun Xue, 2002. "Random paths to stability in the roommate problem," Discussion Papers 0102-65, Columbia University, Department of Economics.
  7. Dutta, B. & Nouweland, C.G.A.M. van den & Tijs, S.H., 2003. "Link formation in cooperative situations," Open Access publications from Tilburg University urn:nbn:nl:ui:12-121826, Tilburg University.
  8. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
  9. Jackson, Matthew O., 1998. "The Evolution of Social and Economic Networks," Working Papers 1044, California Institute of Technology, Division of the Humanities and Social Sciences.
  10. Dutta, Bhaskar & Mutuswami, Suresh, 1997. "Stable Networks," Journal of Economic Theory, Elsevier, vol. 76(2), pages 322-344, October.
    • Dutta, Bhaskar & Mutuswami, Suresh, 1996. "Stable Networks," Working Papers 971, California Institute of Technology, Division of the Humanities and Social Sciences.
  11. Tayfun Sönmez & Tarik Kara, 1997. "Implementation of college admission rules (*)," Economic Theory, Springer, vol. 9(2), pages 197-218.
  12. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, Econometric Society, vol. 58(6), pages 1475-80, November.
  13. Tayfun Sonmez, 1999. "Strategy-Proofness and Essentially Single-Valued Cores," Econometrica, Econometric Society, Econometric Society, vol. 67(3), pages 677-690, May.
  14. Roth, Alvin E, 1991. "A Natural Experiment in the Organization of Entry-Level Labor Markets: Regional Markets for New Physicians and Surgeons in the United Kingdom," American Economic Review, American Economic Association, vol. 81(3), pages 415-40, June.
  15. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
  16. 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, vol. 89(4), pages 748-780, September.
  17. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June.
  18. Alkan, Ahmet, 1988. "Nonexistence of stable threesome matchings," Mathematical Social Sciences, Elsevier, vol. 16(2), pages 207-209, October.
  19. 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.
  20. 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.
  21. Ray, Debraj, 1989. "Credible Coalitions and the Core," International Journal of Game Theory, Springer, vol. 18(2), pages 185-87.
  22. 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, University of Chicago Press, vol. 92(6), pages 991-1016, December.
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 in new window

Cited by:
  1. Bando, Keisuke, 2012. "Many-to-one matching markets with externalities among firms," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 14-20.
  2. Edward Cartwright & Myrna Wooders, 2008. "Behavioral Properties of Correlated Equilibrium; Social Group Structures with Conformity and Stereotyping," Vanderbilt University Department of Economics Working Papers 0814, Vanderbilt University Department of Economics.
  3. N. Roketskiy, 2012. "Farsightedly Stable Matchings," Working Papers 12-26, NET Institute.
  4. Paula Jaramillo & Çagatay Kayi & Flip Klijn, 2012. "On the Exhaustiveness of Truncation and Dropping Strategies in Many-to-Many Matching Markets," Working Papers 632, Barcelona Graduate School of Economics.
  5. Dimitrov, Dinko & Lazarova, Emiliya, 2011. "Two-sided coalitional matchings," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 46-54, July.
  6. Bettina-Elisabeth Klaus & Markus Walzl, 2007. "Stable Many-to-Many Matchings with Contracts," Harvard Business School Working Papers 09-046, Harvard Business School, revised Sep 2008.
  7. Hatfield, John William & Kominers, Scott Duke, 2010. "Matching Networks with Bilateral Contracts," Research Papers 2050, Stanford University, Graduate School of Business.
  8. Hatfield, John William & Kojima, Fuhito, 2010. "Substitutes and stability for matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1704-1723, September.
  9. Robin S. Lee & Michael Schwarz, 2009. "Interviewing in Two-Sided Matching Markets," NBER Working Papers 14922, National Bureau of Economic Research, Inc.
  10. Fuhito Kojima & M. Ünver, 2008. "Random paths to pairwise stability in many-to-many matching problems: a study on market equilibration," International Journal of Game Theory, Springer, vol. 36(3), pages 473-488, March.
  11. Westkamp, Alexander, 2010. "Market structure and matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1724-1738, September.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpga:0309005. 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: (EconWPA).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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.