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Implementation of Stable Solutions to Marriage Problems

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Author Info
José Alcalde () (Universidad de Alicante)

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Abstract

This paper analyzes the possibility of irnplementing stable outcomes for marriage markets. Our first result shows a contradiction between the use of stable mechanisins and the hypotesis of agents' behaviour consiclered in the Nash equilibriurn concept . We analyze the possibility of irnplementing two sets of stable allocations, by employing two types of rnechanisms. The first mechanisrn is a "now-or- never" choice process that permits us to irnplement in undominated Nash equilibria the set of all the stable allocations. The second choice process is the classic algorithm in matching theory, the Gale-Shapley mechanism. A reversal property is observed in such a mechanism when agents act strategically. The use of a mechanism which selects the best solution for one side of the market in the absence of strategic behaviour yields the best stable solution for the agents on the other side under dominance solvability.

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File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-1995-05.pdf
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File Function: Fisrt version / Primera version, 1995
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Publisher Info
Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 1995-05.

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Length: 24 pages
Date of creation: Jan 1995
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:1995-05

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Keywords: Matching markets; Implementation; Stability.;

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  1. Koji Takamiya, 2006. "On the Equivalence of G-weak and -strong Cores in the Marriage Problem," ISER Discussion Paper 0652, Institute of Social and Economic Research, Osaka University, revised Jul 2006. [Downloadable!]
  2. repec:ese:iserwp: is not listed on IDEAS
  3. 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:
  4. 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:
  5. Luis Corchón & Andreu Mas-Colell, 1995. "A Note On Stability Of Best Reply And Gradient Systems With Applications To Imperfectly Competitive Models," Working Papers. Serie AD 1995-18, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
  6. Matteo Triossi & Antonio Romero-Medina, 2006. "Ramón y Cajal: Mediation and Meritocracy," Carlo Alberto Notebooks 22, Collegio Carlo Alberto. [Downloadable!]
  7. David Pérez-Castrillo & Marilda Sotomayor, 2003. "A Selling Mechanism," Revista Brasileira de Economia, Graduate School of Economics, Getulio Vargas Foundation (Brazil), vol. 57(4), April. [Downloadable!]
  8. 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:
  9. Rodrigo Velez & William Thomson, 2009. "Let them cheat!," RCER Working Papers 552, University of Rochester - Center for Economic Research (RCER). [Downloadable!]
  10. José Alcalde & Antonio Romero Medina & David Pérez-Castrillo, 1997. "- Hiring Procedures To Implement Stable Allocations," Working Papers. Serie AD 1997-10, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
    Other versions:
  11. Alexey Kushnir, 2009. "Matching Markets with Signals," Working Papers 2009.39, Fondazione Eni Enrico Mattei. [Downloadable!]
  12. Koji Takamiya, 2006. "Preference Revelation Games and Strong Cores of Allocation Problems with Indivisibilities," ISER Discussion Paper 0651, Institute of Social and Economic Research, Osaka University. [Downloadable!]
  13. Haeinger, Guillaume & Wooders, Myrna, 2003. "Decentralized Job Matching," The Warwick Economics Research Paper Series (TWERPS) 688, University of Warwick, Department of Economics. [Downloadable!]
    Other versions:
  14. David Perez-Castrillo & Marilda Sotomayor, 2000. "A Simple Selling and Buying Procedure," Econometric Society World Congress 2000 Contributed Papers 0704, Econometric Society. [Downloadable!]
    Other versions:
  15. Sang-Chul Suh & Quan Wen, 2008. "Subgame perfect implementation of stable matchings in marriage problems," Social Choice and Welfare, Springer, vol. 31(1), pages 163-174, June. [Downloadable!] (restricted)
  16. José Alcalde, 1995. "Exchange-Proofness or Divorce-Proofness? Stability in One-Sided Matching Markets," Working Papers. Serie AD 1995-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
    Other versions:
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