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Manipulation via Capacities Revisited

  • EHLERS, Lars

This paper revisits manipulation via capacities in centralized two-sided matching markets. Sönmez (1997) showed that no stable mechanism is nonmanipulable via capacities. We show that non-manipulability via capacities can be equivalently described by two types of non-manipulation via capacities: non-Type-I-manipulability meaning that no college with vacant positions can manipulate by dropping some of its empty positions; and non-Type-II manipulability meaning that no college with no vacant positions can manipulate by dropping some of its filled positions. Our main result shows that the student-optimal stable mechanism is the unique stable mechanism which is non-Type-I-manipulable via capacities and independent of truncations. Our characterization supports the use of the student-optimal stable mechanism in these matching markets because of its limited manipulability via capacities by colleges.

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Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2009-03.

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Length: 24 pages
Date of creation: 2009
Date of revision:
Handle: RePEc:mtl:montde:2009-03
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  1. Antonio Romero-Medina & Matteo Triossi, 2011. "Games with Capacity Manipulation: Incentives and Nash Equilibria," Documentos de Trabajo 280, Centro de Economía Aplicada, Universidad de Chile.
  2. Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, vol. 77(1), pages 197-204, November.
  3. 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.
  4. Parag A. Pathak & Tayfun Sönmez, 2013. "School Admissions Reform in Chicago and England: Comparing Mechanisms by Their Vulnerability to Manipulation," American Economic Review, American Economic Association, vol. 103(1), pages 80-106, February.
  5. Hideo Konishi & M. Ünver, 2006. "Games of Capacity Manipulation in Hospital-intern Markets," Social Choice and Welfare, Springer, vol. 27(1), pages 3-24, August.
  6. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January.
  7. José Alcalde, 1995. "Implementation of Stable Solutions to Marriage Problems," Working Papers. Serie AD 1995-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  8. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882.
  9. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
  10. Kojima Fuhito, 2007. "When Can Manipulations be Avoided in Two-Sided Matching Markets? -- Maximal Domain Results," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-18, September.
  11. Fuhito Kojima, 2006. "Mixed Strategies in Games of Capacity Manipulation in Hospital–Intern Markets," Social Choice and Welfare, Springer, vol. 27(1), pages 25-28, August.
  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.
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