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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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    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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