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Implementation of college admission rules (*)

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Author Info
Tayfun Sönmez (Department of Economics, University of Michigan, Ann Arbor, MI 48109, USA)
Tarik Kara (Department of Economics, University of Rochester, Rochester, NY 14627, USA)

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Abstract

We consider both Nash and strong Nash implementation of various matching rules for college admissions problems. We show that all such rules are supersolutions of the stable rule. Among these rules the "lower bound" stable rule is implementable in both senses. The "upper bound" Pareto and individually rational rule is strong Nash implementable yet it is not Nash implementable. Two corollaries of interest are the stable rule is the minimal (Nash or strong Nash) implementable solution that is Pareto optimal and individually rational, and the stable rule is the minimal (Nash or strong Nash) implementable extension of any of its subsolutions.

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Publisher Info
Article provided by Springer in its journal Economic Theory.

Volume (Year): 9 (1997)
Issue (Month): 2 ()
Pages: 197-218
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Handle: RePEc:spr:joecth:v:9:y:1997:i:2:p:197-218

Note: Received: August 22, 1994; revised version July 6, 1995
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Find related papers by JEL classification:
C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy-Making and Implementation

Cited by:
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  1. Claus-Jochen Haake & Bettina-Elisabeth Klaus, 2008. "Stability and Nash Implementation in Matching Markets with Couples," Harvard Business School Working Papers 09-017, Harvard Business School. [Downloadable!]
    Other versions:
  2. Kaniska Dam & David Perez-Castrillo, 2003. "The Principal-Agent Matching Market," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
    Other versions:
  3. 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. [Downloadable!]
    Other versions:
  4. Claus-Jochen Haake & Bettina Klaus, 2009. "Monotonicity and Nash implementation in matching markets with contracts," Economic Theory, Springer, vol. 41(3), pages 393-410, December. [Downloadable!] (restricted)
    Other versions:
  5. José Alcalde & Antonio Romero Medina, 1999. "- Sequential Decisions In The College Admissions Problem," Working Papers. Serie AD 1999-16, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
    Other versions:
  6. Hideo Konishi & M. Utku Ünver, 2003. "Credible Group Stability in Multi-Partner Matching Problems," Working Papers 2003.115, Fondazione Eni Enrico Mattei. [Downloadable!]
    Other versions:
  7. 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. [Downloadable!] (restricted)
    Other versions:
  8. Haluk Ergin & Tayfun Sönmez, 2005. "Games of School Choice under the Boston Mechanism," Boston College Working Papers in Economics 619, Boston College Department of Economics. [Downloadable!]
    Other versions:
  9. Matteo Triossi & Antonio Romero-Medina, 2006. "Ramón y Cajal: Mediation and Meritocracy," Carlo Alberto Notebooks 22, Collegio Carlo Alberto. [Downloadable!]
  10. José Alcalde & Pablo Revilla, 1998. "- The Role Of Unions In Hiring Procedures For Job Markets," Working Papers. Serie AD 1998-02, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
    Other versions:
  11. repec:bep:theadv:v:2:y:2006:i:1:p:1257-1257 is not listed on IDEAS
  12. Guillaume Haeringer & Flip Klijn, 2006. "Constrained School Choice," UFAE and IAE Working Papers 671.06, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 02 Dec 2008. [Downloadable!]
    Other versions:
  13. Manabu Toda, 2006. "Monotonicity and Consistency in Matching Markets," International Journal of Game Theory, Springer, vol. 34(1), pages 13-31, April. [Downloadable!] (restricted)
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