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Matching markets with middlemen under transferable utility

Author

Listed:
  • Ata Atay

    (University of Barcelona, and Barcelona Economic Analysis Team (BEAT))

  • Eric Bahel

    (Virginia Polytechnic Institute and State University
    National Science Foundation)

  • Tamás Solymosi

    (Corvinus University of Budapest)

Abstract

This paper studies matching markets in the presence of middlemen. In our framework, a buyer–seller pair may either trade directly or use the services of a middleman; and a middleman may serve multiple buyer–seller pairs. For each such market, we examine the associated TU game. We first show that, in our context, an optimal matching can be obtained by considering the two-sided assignment market where each buyer–seller pair is allowed to use the mediation services of any middleman free of charge. Second, we prove that matching markets with middlemen are totally balanced: in particular, we show the existence of a buyer-optimal (seller-optimal) core allocation where each buyer (seller) receives her marginal contribution to the grand coalition. In general, the core does not exhibit a middleman-optimal allocation, not even when there are only two buyers and two sellers. However, we prove that in these small markets the maximum core payoff to each middleman is her marginal contribution. Finally, we establish the coincidence between the core and the set of competitive equilibrium payoff vectors.

Suggested Citation

  • Ata Atay & Eric Bahel & Tamás Solymosi, 2023. "Matching markets with middlemen under transferable utility," Annals of Operations Research, Springer, vol. 322(2), pages 539-563, March.
    • Handle: RePEc:spr:annopr:v:322:y:2023:i:2:d:10.1007_s10479-022-05111-6
    DOI: 10.1007/s10479-022-05111-6
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    More about this item

    Keywords

    Assignment games; Core; Competitive equilibrium; Matching markets; Matchmakers; Middlemen;
    All these keywords.

    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
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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