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Acyclicity and singleton cores in matching markets

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  • Romero-Medina, Antonio
  • Triossi, Matteo

Abstract

This paper analyzes the role of acyclicity in singleton cores. We show that the absence of simultaneous cycles is a sufficient condition for the existence of singleton cores. Furthermore, acyclicity in the preferences of either side of the market is a minimal condition that guarantees the existence of singleton cores. If firms or workers preferences are acyclical, unique stable matching is obtained through a procedure that resembles a serial dictatorship. Thus, acyclicity generalizes the notion of common preferences. It follows that if the firms or workers preferences are acyclical, unique stable matching is strongly efficient for the other side of the market

Suggested Citation

  • Romero-Medina, Antonio & Triossi, Matteo, 2011. "Acyclicity and singleton cores in matching markets," UC3M Working papers. Economics we1126, Universidad Carlos III de Madrid. Departamento de Economía.
  • Handle: RePEc:cte:werepe:we1126
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    7. Alejandra Mizala & Pilar Romaguera & Sebastian Gallegos, 2010. "Public-Private Wage Gap In Latin America (1999-2007): A Matching Approach," Documentos de Trabajo 268, Centro de Economía Aplicada, Universidad de Chile.
    8. Eeckhout, Jan, 2000. "On the uniqueness of stable marriage matchings," Economics Letters, Elsevier, vol. 69(1), pages 1-8, October.
    9. Antonio Romero-Medina & Matteo Triossi, 2013. "Games with capacity manipulation: incentives and Nash equilibria," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 701-720, September.
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    Citations

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    Cited by:

    1. Tello Benjamín, 2017. "Stability of Equilibrium Outcomes under Deferred Acceptance: Acyclicity and Dropping Strategies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 17(2), pages 1-9, June.
    2. Akahoshi, Takashi, 2014. "Singleton core in many-to-one matching problems," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 7-13.
    3. Estelle Cantillon & Li Chen & Juan Sebastian Pereyra Barreiro, 2022. "Respecting priorities versus respecting preferences in school choice: When is there a trade-off ?," Working Papers ECARES 2022-39, ULB -- Universite Libre de Bruxelles.
    4. Chen, Yajing & Jiao, Zhenhua & Zhang, Yang & Zhao, Fang, 2021. "Resource allocation on the basis of priorities under multi-unit demand," Economics Letters, Elsevier, vol. 202(C).
    5. Antonio Romero-Medina & Matteo Triossi, 2021. "Two-sided strategy-proofness in many-to-many matching markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 105-118, March.
    6. Gregory Z. Gutin & Philip R. Neary & Anders Yeo, 2021. "Unique Stable Matchings," Papers 2106.12977, arXiv.org, revised Jul 2023.
    7. Gutin, Gregory Z. & Neary, Philip R. & Yeo, Anders, 2023. "Unique stable matchings," Games and Economic Behavior, Elsevier, vol. 141(C), pages 529-547.
    8. Jaeok Park, 2015. "Competitive Equilibrium and Singleton Cores in Generalized Matching Problems (published in:International Journal of Game Theory, May 2017, Vol.46, Issue2, 487-509)," Working papers 2015rwp-85, Yonsei University, Yonsei Economics Research Institute.
    9. Jaeok Park, 2017. "Competitive equilibrium and singleton cores in generalized matching problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 487-509, May.
    10. Karpov, Alexander, 2019. "A necessary and sufficient condition for uniqueness consistency in the stable marriage matching problem," Economics Letters, Elsevier, vol. 178(C), pages 63-65.
    11. Takashi Akahoshi, 2014. "A necessary and sufficient condition for stable matching rules to be strategy-proof," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(3), pages 683-702, October.
    12. Wu, Qinggong, 2015. "A finite decentralized marriage market with bilateral search," Journal of Economic Theory, Elsevier, vol. 160(C), pages 216-242.
    13. Estelle Cantillon & Li Chen & Juan S. Pereyra, 2022. "Respecting priorities versus respecting preferences in school choice: When is there a trade-off?," Papers 2212.02881, arXiv.org, revised Jan 2024.
    14. Antonio Romero-Medina & Matteo Triossi, 2013. "Games with capacity manipulation: incentives and Nash equilibria," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 701-720, September.

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    More about this item

    Keywords

    Stable matching;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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