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Competitive Equilibrium and Singleton Cores in Generalized Matching Problems (published in:International Journal of Game Theory, May 2017, Vol.46, Issue2, 487-509)

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  • Jaeok Park

    (Yonsei University)

Abstract

We study competitive equilibria in generalized matching problems. We show that, if there is a competitive matching, then it is unique and the core is a singleton consisting of the competitive matching. That is, a singleton core is necessary for the existence of competitive equilibria. We also show that a competitive matching exists if and only if the matching produced by the top trading cycles algorithm is feasible, in which case it is the unique competitive matching. Hence, we can use the top trading cycles algorithm to test whether a competitive equilibrium exists and to construct a competitive equilibrium if one exists. Lastly, in the context of bilateral matching problems, we compare the condition for the existence of competitive matchings with existing suffcient conditions for the existence or uniqueness of stable matchings and show that it is weaker than the existing conditions.

Suggested Citation

  • 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.
    • Handle: RePEc:yon:wpaper:2015rwp-85
    as

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    References listed on IDEAS

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    1. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    2. Jens Gudmundsson, 2014. "When do stable roommate matchings exist? A review," Review of Economic Design, Springer;Society for Economic Design, vol. 18(2), pages 151-161, June.
    3. Alvin E. Roth, 2007. "Repugnance as a Constraint on Markets," Journal of Economic Perspectives, American Economic Association, vol. 21(3), pages 37-58, Summer.
    4. Alvaro Rodrigues-Neto, Jose, 2007. "Representing roommates' preferences with symmetric utilities," Journal of Economic Theory, Elsevier, vol. 135(1), pages 545-550, July.
    5. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October.
    6. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 135-153.
    7. Romero-Medina, Antonio & Triossi, Matteo, 2013. "Acyclicity and singleton cores in matching markets," Economics Letters, Elsevier, vol. 118(1), pages 237-239.
    8. Sotomayor, Marilda, 2007. "Connecting the cooperative and competitive structures of the multiple-partners assignment game," Journal of Economic Theory, Elsevier, vol. 134(1), pages 155-174, May.
    9. Kesten, Onur, 2006. "On two competing mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, vol. 127(1), pages 155-171, March.
    10. Bikhchandani, Sushil & Mamer, John W., 1997. "Competitive Equilibrium in an Exchange Economy with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 74(2), pages 385-413, June.
    11. José Alcalde, 1994. "Exchange-proofness or divorce-proofness? Stability in one-sided matching markets," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 275-287, December.
    12. Sonmez, Tayfun, 1996. "Implementation in generalized matching problems," Journal of Mathematical Economics, Elsevier, vol. 26(4), pages 429-439.
    13. Parag A. Pathak & Tayfun Sonmez, 2008. "Leveling the Playing Field: Sincere and Sophisticated Players in the Boston Mechanism," American Economic Review, American Economic Association, vol. 98(4), pages 1636-1652, September.
    14. Muriel Niederle & Leeat Yariv, 2009. "Decentralized Matching with Aligned Preferences," NBER Working Papers 14840, National Bureau of Economic Research, Inc.
    15. Roth, Alvin E. & Postlewaite, Andrew, 1977. "Weak versus strong domination in a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 131-137, August.
    16. Edgeworth, Francis Ysidro, 1881. "Mathematical Psychics," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number edgeworth1881.
    17. Ma, Jinpeng, 1994. "Strategy-Proofness and the Strict Core in a Market with Indivisibilities," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 75-83.
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    More about this item

    Keywords

    matching; competitive equilibrium; core; top trading cycles algorithm;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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