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Multiproduct Firms and Discrete Choice Models of Demand: Existence and Uniqueness of the Bertrand-Nash Equilibrium

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  • Thomas Favory

    (Economics Discipline, Business School, University of Western Australia)

Abstract

This paper proves the existence and uniqueness of Bertrand-Nash equilibrium in oligopolies, where each firm may sell multiple substitutes of the same good. Bertrand competition emerges as a limit case when the number of products per firm increases if the consumers’ willingness to pay for products follow a sufficiently slim-tailed distribution. In opposition, the double exponential distribution is not slim enough, and firms conserve monopolistic power even for an arbitrarily large number of products per firm. Moreover, the double exponential distribution provides closed-form solutions that relate to discrete choice theory. First, a duality with representative consumers helps recover multinomial logit (MNL) demand functions and constant elasticity of substitution (CES) utility functions. Second, the game in which firms sequentially set the quality, then the price of their products, has a unique equilibrium.

Suggested Citation

  • Thomas Favory, 2020. "Multiproduct Firms and Discrete Choice Models of Demand: Existence and Uniqueness of the Bertrand-Nash Equilibrium," Economics Discussion / Working Papers 20-24, The University of Western Australia, Department of Economics.
    • Handle: RePEc:uwa:wpaper:20-24
    Note: MD5 = 59d12f727f2139d91d3882c35cb8433a
    as

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    File URL: https://ecompapers.biz.uwa.edu.au/paper/PDF%20of%20Discussion%20Papers/2020/DP%2020.24_Favory.pdf
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    References listed on IDEAS

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    Cited by:

    1. Schuur, Peter & Badur, Bertan & Sencer, Asli, 2021. "An explicit Nash equilibrium for a market share attraction game," Operations Research Perspectives, Elsevier, vol. 8(C).

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    More about this item

    Keywords

    Multiproduct firms; Price competition; Oligopoly; Discrete choice; Product differentiation;
    All these keywords.

    JEL classification:

    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L12 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Monopoly; Monopolization Strategies
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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