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On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets

  • Paula Jaramillo

    ()

  • Kagi Cagatay

    ()

  • Flip Klijn

    ()

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 reshu_ing).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, truncation strategies are exhaustive for each agent with quota 1 (Theorem 1). We show that this result cannot be extended neither to group manipulations (even when all quotas equal 1 - Example 1), nor to individual manipulations when the agent's quota is larger than 1 (even when all other agents' quotas equal 1 - Example 2). Finally, we prove that for each stable mechanism, dropping strategies are exhaustive for each group of agents on the same side of the market (Theorem 2), i.e., independently of the quotas.

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Paper provided by UNIVERSIDAD DEL ROSARIO in its series DOCUMENTOS DE TRABAJO with number 009997.

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Length: 19
Date of creation: 26 Sep 2012
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Handle: RePEc:col:000092:009997
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  1. Sotomayor, Marilda, 2004. "Implementation in the many-to-many matching market," Games and Economic Behavior, Elsevier, vol. 46(1), pages 199-212, January.
  2. 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).
  3. Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 55-70, July.
  4. 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.
  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. Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, vol. 77(1), pages 197-204, November.
  7. Klaus Bettina & Walzl Markus, 2006. "Stable Many-to-Many Matchings with Contracts," Research Memorandum 042, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  8. 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).
  9. Ahmet Alkan, 2002. "A class of multipartner matching markets with a strong lattice structure," Economic Theory, Springer, vol. 19(4), pages 737-746.
  10. 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.
  11. Marilda Sotomayor, 1999. "The lattice structure of the set of stable outcomes of the multiple partners assignment game," International Journal of Game Theory, Springer, vol. 28(4), pages 567-583.
  12. Flip Klijn, 2011. "A Many-to-Many 'Rural Hospital Theorem'," UFAE and IAE Working Papers 877.11, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  13. 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.
  14. 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.
  15. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
  16. Roth, Alvin E & Sotomayor, Marilda, 1989. "The College Admissions Problem Revisited," Econometrica, Econometric Society, vol. 57(3), pages 559-70, May.
  17. Ahmet Alkan, 2001. "original papers : On preferences over subsets and the lattice structure of stable matchings," Review of Economic Design, Springer, vol. 6(1), pages 99-111.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. 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.
  23. 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.
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