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Full substitutability

Author

Listed:
  • Hatfield, John William

    (McCombs School of Business, University of Texas at Austin)

  • Kominers, Scott Duke

    (Entrepreneurial Management Unit, Department of Economics, and Center of Mathematical Sciences and Applications, Harvard University)

  • Nichifor, Alexandru

    (Economics Department, University of Melbourne)

  • Ostrovsky, Michael

    (Graduate School of Business, Stanford University)

  • Westkamp, Alexander

    (Department of Management, Economics and Social Sciences, University of Cologne)

Abstract

Various forms of substitutability are essential for establishing the existence of equilibria and other useful properties in diverse settings such as matching, auctions, and exchange economies with indivisible goods. We extend earlier models' definitions of substitutability to settings in which each agent can be both a buyer in some transactions and a seller in others, and show that all these definitions are equivalent. We then introduce a new class of substitutable preferences that allows us to model intermediaries with production capacity. We also prove that substitutability is preserved under economically important transformations such as trade endowments, mergers, and limited liability.

Suggested Citation

  • Hatfield, John William & Kominers, Scott Duke & Nichifor, Alexandru & Ostrovsky, Michael & Westkamp, Alexander, 2019. "Full substitutability," Theoretical Economics, Econometric Society, vol. 14(4), November.
    • Handle: RePEc:the:publsh:3240
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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Jonathan Ma & Scott Duke Kominers, 2018. "Bundling Incentives in (Many-to-Many) Matching with Contracts," Harvard Business School Working Papers 19-011, Harvard Business School.
    2. Dimakopoulos, Philipp D. & Heller, C.-Philipp, 2018. "Matching with Waiting Times: The German Entry-Level Labor Market for Lawyers," Rationality and Competition Discussion Paper Series 68, CRC TRR 190 Rationality and Competition.
    3. Jagadeesan, Ravi & Kominers, Scott Duke & Rheingans-Yoo, Ross, 2018. "Strategy-proofness of worker-optimal matching with continuously transferable utility," Games and Economic Behavior, Elsevier, vol. 108(C), pages 287-294.
    4. Schlegel, Jan Christoph, 2022. "The structure of equilibria in trading networks with frictions," Theoretical Economics, Econometric Society, vol. 17(2), May.
    5. Lukas Hümbs & Alexander Martin & Lars Schewe, 2022. "Exploiting complete linear descriptions for decentralized power market problems with integralities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(3), pages 451-474, June.
    6. Elizabeth Baldwin & Paul Klemperer, 2019. "Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities," Econometrica, Econometric Society, vol. 87(3), pages 867-932, May.
    7. Yang, Yi-You, 2013. "Competitive equilibrium with indivisible objects," MPRA Paper 74662, University Library of Munich, Germany, revised 19 Oct 2016.
    8. Candogan, Ozan & Epitropou, Markos & Vohra, Rakesh V., 2016. "Competitive Equilibrium and Trading Networks: A Network Flow Approach," Economics Series 323, Institute for Advanced Studies.
    9. Kazuo Murota, 2016. "Discrete convex analysis: A tool for economics and game theory," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 151-273, December.
    10. Koji Yokote, 2020. "On optimal taxes and subsidies: A discrete saddle-point theorem with application to job matching under constraints," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 5(1), pages 37-77, December.
    11. Yokote, Koji, 2023. "A critical comparison between the gross substitutes and complements conditions," Economics Letters, Elsevier, vol. 226(C).
    12. Delacrétaz, David & Kominers, Scott Duke & Nichifor, Alexandru, 2020. "Comparative statics for size-dependent discounts in matching markets," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 127-131.

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    More about this item

    Keywords

    Matching with contracts; substitutability; trading networks;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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