On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets
We consider two-sided many-to-many matching markets in which each worker may work for multiple firms and each firm may hire multiple workers. We study individual and group manipulations in centralized markets that employ (pairwise) stable mechanisms and that require participants to submit rank order lists of agents on the other side of the market. We are interested in simple preference manipulations that have been reported and studied in empirical and theoretical work: truncation strategies, which are the lists obtained by removing a tail of least preferred partners from a preference list, and the more general dropping strategies, which are the lists obtained by only removing partners from a preference list (i.e., no reshuffling). We study when truncation/dropping strategies are exhaustive for a group of agents on the same side of the market, i.e., when each match resulting from preference manipulations can be replicated or improved upon by some truncation/dropping strategies. We prove that for each stable mechanism, dropping strategies are exhaustive for each group of agents on the same side of the market (Theorem 1), i.e., independently of the quotas. Then, we show that for each stable mechanism, truncation strategies are exhaustive for each agent with quota 1 (Theorem 2). Finally, we show that this result cannot be extended neither to individual manipulations when the agent’s quota is larger than 1 (even when all other agents’ quotas equal 1—Example 1), nor to group manipulations (even when all quotas equal 1—Example 2). Copyright Springer-Verlag Berlin Heidelberg 2014
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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 42 (2014)
Issue (Month): 4 (April)
|Contact details of provider:|| Web page: http://www.unicaen.fr/recherche/mrsh/scw/|
More information through EDIRC
|Order Information:||Web: http://www.springer.com/economics/economic+theory/journal/355|
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.:
- Assaf Romm, 2014. "Implications of capacity reduction and entry in many-to-one stable matching," Social Choice and Welfare, The Society for Social Choice and Welfare, vol. 43(4), pages 851-875, December.
- Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
- Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 55-70, July.
- 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.
- Ma, Jinpeng, 2010. "The singleton core in the college admissions problem and its application to the National Resident Matching Program (NRMP)," Games and Economic Behavior, Elsevier, vol. 69(1), pages 150-164, May.
- Ruth Mart?ez & Jordi MassóAuthor-Name: Alejandro Neme & Jorge Oviedo, . "An Algorithm To Compute The Set Of Many-To-Many Stable Matchings," UFAE and IAE Working Papers 457.00, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Flip Klijn & Ayse Yazici, 2014.
"A Many-to-Many "Rural Hospital Theorem","
567, Barcelona Graduate School of Economics.
- Roth, Alvin E & Sotomayor, Marilda, 1989. "The College Admissions Problem Revisited," Econometrica, Econometric Society, vol. 57(3), pages 559-70, May.
- Echenique, Federico & Oviedo, Jorge, 2006.
"A theory of stability in many-to-many matching markets,"
Econometric Society, vol. 1(2), pages 233-273, June.
- Jorge Oviedo & Federico Echenique, 2005. "A Theory of Stability in Many-to-Many Matching Markets," 2005 Meeting Papers 233, Society for Economic Dynamics.
- Echenique, Federico & Oviedo, Jorge, 2003. "A Theory of Stability in Many-to-Many Matching Markets," Working Papers 1185, California Institute of Technology, Division of the Humanities and Social Sciences.
- Federico Echenique & Jorge Oviedo, 2004. "A Theory of Stability in Many-to-many Matching Markets," Game Theory and Information 0401002, EconWPA.
- Federico Echenique & Jorge Oviedo, 2003. "A Theory of Stability in Many-to-many Matching Markets," Levine's Working Paper Archive 666156000000000374, David K. Levine.
- Konishi, Hideo & Unver, M. Utku, 2006.
"Credible group stability in many-to-many matching problems,"
Journal of Economic Theory,
Elsevier, vol. 129(1), pages 57-80, July.
- Hideo Konishi & M. Utku Unver, 2003. "Credible Group-Stability in Many-to-Many Matching Problems," Boston College Working Papers in Economics 570, Boston College Department of Economics, revised 19 Jan 2005.
- Hideo Konishi & M. Utku Ünver, 2003. "Credible Group Stability in Many-to-Many Matching Problems," Game Theory and Information 0309005, EconWPA, revised 06 Sep 2003.
- Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, vol. 99(3), pages 608-27, June.
- Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2004. "An algorithm to compute the full set of many-to-many stable matchings," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 187-210, March.
- Klaus Bettina & Walzl Markus, 2006.
"Stable Many-to-Many Matchings with Contracts,"
042, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, vol. 77(1), pages 197-204, November.
- Alvin E. Roth & Uriel G. Rothblum, 1999. "Truncation Strategies in Matching Markets--In Search of Advice for Participants," Econometrica, Econometric Society, vol. 67(1), pages 21-44, January.
- Itai Ashlagi & Flip Klijn, 2010.
"Manipulability in Matching Markets: Conflict and Coincidence of Interests,"
UFAE and IAE Working Papers
835.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Itai Ashlagi & Flip Klijn, 2012. "Manipulability in matching markets: conflict and coincidence of interests," Social Choice and Welfare, The Society for Social Choice and Welfare, vol. 39(1), pages 23-33, June.
- Itai Ashlagi & Flip Klijn, 2010. "Manipulability in Matching Markets: Conflict and Coincidence of Interests," Working Papers 479, Barcelona Graduate School of Economics.
- Ahmet Alkan, 2001. "original papers : On preferences over subsets and the lattice structure of stable matchings," Review of Economic Design, Society for Economic Design, vol. 6(1), pages 99-111.
- Mongell, Susan & Roth, Alvin E, 1991. "Sorority Rush as a Two-Sided Matching Mechanism," American Economic Review, American Economic Association, vol. 81(3), pages 441-64, June.
- 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.
- 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.
- Sotomayor, Marilda, 2004. "Implementation in the many-to-many matching market," Games and Economic Behavior, Elsevier, vol. 46(1), pages 199-212, January.
- 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.
- Marilda Sotomayor, 1999. "The lattice structure of the set of stable outcomes of the multiple partners assignment game," International Journal of Game Theory, Game Theory Society, vol. 28(4), pages 567-583.
- Ahmet Alkan, 2002. "A class of multipartner matching markets with a strong lattice structure," Economic Theory, Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 737-746.
When requesting a correction, please mention this item's handle: RePEc:spr:sochwe:v:42:y:2014:i:4:p:793-811. 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: (Sonal Shukla)or (Rebekah McClure)
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.