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Competitive Equilibria in Two-Sided Matching Markets with General Utility Functions

Author

Listed:
  • Saeed Alaei

    (Google Inc, 1600 Amphitheatre Parkway, Mountain View, California 94043)

  • Kamal Jain

    (Faira, Kirkland, Washington 98033)

  • Azarakhsh Malekian

    (Rotman School of Management, University of Toronto, Toronto, Ontario)

Abstract

We present an exact characterization of utilities in competitive equilibria of two-sided matching markets in which the utility of each agent depends on the choice of partner and the terms of the partnership, potentially including monetary transfer. Examples of such markets include sellers and buyers or jobs and workers. Demange and Gale showed that the set of competitive equilibria in this type of market forms a complete lattice with each extreme point of the lattice representing an equilibrium with the highest utilities for the agents on one side and the lowest utilities for the agents on the opposite side.Our characterization is based on establishing a connection between the competitive equilibria of a market and the competitive equilibria of certain strict subsets of that market—each obtained by removing exactly one agent. This characterization captures the effect of competition when agents are added to the market or removed from the market. It gives a precise procedure for constructing competitive equilibria and provides a constructive proof of existence of such equilibria; in contrast, previous proofs have been based on fixed point theorems.

Suggested Citation

  • Saeed Alaei & Kamal Jain & Azarakhsh Malekian, 2016. "Competitive Equilibria in Two-Sided Matching Markets with General Utility Functions," Operations Research, INFORMS, vol. 64(3), pages 638-645, June.
    • Handle: RePEc:inm:oropre:v:64:y:2016:i:3:p:638-645
    DOI: 10.1287/opre.2016.1509
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    References listed on IDEAS

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    Cited by:

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    2. Edward Anderson & David Gamarnik & Anton Kleywegt & Asuman Ozdaglar, 2016. "Preface to the Special Issue on Information and Decisions in Social and Economic Networks," Operations Research, INFORMS, vol. 64(3), pages 561-563, June.
    3. Yu Zhou & Shigehiro Serizawa, 2019. "Minimum price equilibrium in the assignment market," ISER Discussion Paper 1047, Institute of Social and Economic Research, Osaka University.
    4. Andersson, Tommy & Svensson, Lars-Gunnar, 2018. "Sequential rules for house allocation with price restrictions," Games and Economic Behavior, Elsevier, vol. 107(C), pages 41-59.
    5. Zhou, Yu & Serizawa, Shigehiro, 2018. "Strategy-proofness and efficiency for non-quasi-linear and common-tiered-object preferences: Characterization of minimum price rule," Games and Economic Behavior, Elsevier, vol. 109(C), pages 327-363.
    6. Eleni Batziou & Martin Bichler & Maximilian Fichtl, 2022. "Core-Stability in Assignment Markets with Financially Constrained Buyers," Papers 2205.06132, arXiv.org.
    7. Mohammad Rasouli & Michael I. Jordan, 2021. "Data Sharing Markets," Papers 2107.08630, arXiv.org, revised Jul 2021.
    8. David Cantala & Damián Gibaja, 2018. "On uniqueness of equilibrium prices in a Bayesian assignment game," Serie documentos de trabajo del Centro de Estudios Económicos 2018-06, El Colegio de México, Centro de Estudios Económicos.

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