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Competitive equilibrium and singleton cores in generalized matching problems

Jaeok Park ()
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Jaeok Park: Yonsei University

International Journal of Game Theory, 2017, vol. 46, issue 2, 487-509

Abstract: 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 sufficient conditions for the existence or uniqueness of stable matchings and show that it is weaker than most existing conditions for uniqueness.

Keywords: Matching; Competitive equilibrium; Core; Top trading cycles algorithm (search for similar items in EconPapers)
JEL-codes: C78 D51 (search for similar items in EconPapers)
Date: 2017
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