On the foundation of monopoly in bilateral exchange

Busetto, F., Codognato, G., Ghosal, S. and Turchet, D. (2023) On the foundation of monopoly in bilateral exchange. International Journal of Game Theory, (doi: 10.1007/s00182-023-00847-2) (Early Online Publication)

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.

• Item Type: Articles
• Additional Information: Damiano Turchet gratefully acknowledges financial support from the Economic and Social Research Council [ES/P000681/1].
• Status: Early Online Publication
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Turchet, Mr Damiano and Ghosal, Professor Sayantan
• Authors: Busetto, F., Codognato, G., Ghosal, S., and Turchet, D.
• College/School: College of Social Sciences > Adam Smith Business School; College of Social Sciences > Adam Smith Business School > Economics
• Journal Name: International Journal of Game Theory
• Publisher: Springer
• ISSN: 0020-7276
• ISSN (Online): 1432-1270
• Published Online: 11 May 2023
• Copyright Holders: Copyright © 2022 The Authors
• First Published: First published in International Journal of Game Theory 2023
• Publisher Policy: Reproduced under a Creative Commons License

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
303166		Scottish Graduate School Science Doctoral Training Partnership (DTP)	Mary Beth Kneafsey	Economic and Social Research Council (ESRC)	ES/P000681/1	SS - Academic & Student Administration