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On the foundation of monopoly in bilateral exchange

Author

Listed:
  • Francesca Busetto

    (Università degli Studi di Udine)

  • Giulio Codognato

    (Università degli Studi di Udine
    Univ Paris Nanterre, CNRS)

  • Sayantan Ghosal

    (University of Glasgow)

  • Damiano Turchet

    (University of Warwick)

Abstract

We address the problem of monopoly in general equilibrium in a mixed version of a monopolistic two-commodity exchange economy where the monopolist, represented as an atom, is endowed with one commodity and “small traders,” represented by an atomless part, are endowed only with the other. First we provide an economic theoretical foundation of the monopoly solution in this bilateral framework through a formalization of an explicit trading process inspired by Pareto (Cours d’économie politique. F. Rouge Editeur, Lausanne, 1896) for an exchange economy with a finite number of commodities, and we give the conditions under which our monopoly solution has the geometric characterization proposed by Schydlowsky and Siamwalla (Q J Econ 80:147–153, 1966). Then, we provide a game theoretical foundation of our monopoly solution through a two-stage reformulation of our model. This allows us to prove that the set of the allocations corresponding to a monopoly equilibrium and the set of the allocations corresponding to a subgame perfect equilibrium of the two-stage game coincide. Finally, we compare our model of monopoly with a bilateral exchange version of a pioneering model proposed by Forchheimer (Jahrbuch für Gesetzgebung, Verwaltung und Volkswirschafts im Deutschen Reich 32:1–12, 1908), known as a model of “partial monopoly” since there a monopolist shares a market with a“competitive fringe.” Journal of Economic Literature Classification Numbers: D42, D51.

Suggested Citation

  • Francesca Busetto & Giulio Codognato & Sayantan Ghosal & Damiano Turchet, 2023. "On the foundation of monopoly in bilateral exchange," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(4), pages 1261-1290, December.
    • Handle: RePEc:spr:jogath:v:52:y:2023:i:4:d:10.1007_s00182-023-00847-2
    DOI: 10.1007/s00182-023-00847-2
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    1. Francesca Busetto & Giulio Codognato & Sayantan Ghosal & Ludovic Julien & Simone Tonin, 2020. "Existence and optimality of Cournot–Nash equilibria in a bilateral oligopoly with atoms and an atomless part," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 933-951, December.
    2. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan, 2011. "Noncooperative oligopoly in markets with a continuum of traders," Games and Economic Behavior, Elsevier, vol. 72(1), pages 38-45, May.
    3. Codognato, Giulio & Ghosal, Sayantan, 2000. "Cournot-Nash equilibria in limit exchange economies with complete markets and consistent prices," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 39-53, August.
    4. Daniel M. Schydlowsky & Ammar Siamwalla, 1966. "Monopoly Under General Equilibrium: A Geometric Exercise," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 80(1), pages 147-153.
    5. Greenberg, J. & Shitovitz, B., 1977. "Advantageous monopolies," LIDAM Reprints CORE 330, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    10. Busetto, Francesca & Codognato, Giulio & Ghosal, Syantan, 2008. "Cournot-Walras Equilibrium as a Subgame Perfect Equilibrium," Economic Research Papers 269786, University of Warwick - Department of Economics.
    11. Sadanand, V., 1988. "Endogenously determined price-setting monopoly in an exchange economy," Journal of Economic Theory, Elsevier, vol. 46(1), pages 172-178, October.
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    More about this item

    JEL classification:

    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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