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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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    1. Jeffrey M. Perloff & Steven C. Salop, 1985. "Equilibrium with Product Differentiation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(1), pages 107-120.
    2. Gianmarco I. P. Ottaviano & Jacques‐François Thisse, 2011. "Monopolistic Competition, Multiproduct Firms And Product Diversity," Manchester School, University of Manchester, vol. 79(5), pages 938-951, September.
    3. Mark Armstrong & John Vickers, 2018. "Multiproduct Pricing Made Simple," Journal of Political Economy, University of Chicago Press, vol. 126(4), pages 1444-1471.
    4. Anderson, Simon P & de Palma, Andre, 1992. "Multiproduct Firms: A Nested Logit Approach," Journal of Industrial Economics, Wiley Blackwell, vol. 40(3), pages 261-276, September.
    5. Dixit, Avinash K & Stiglitz, Joseph E, 1977. "Monopolistic Competition and Optimum Product Diversity," American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.
    6. Volker Nocke & Nicolas Schutz, 2018. "Multiproduct‐Firm Oligopoly: An Aggregative Games Approach," Econometrica, Econometric Society, vol. 86(2), pages 523-557, March.
    7. Anderson, Simon Peter & de Palma, Andre & Thisse, Jacques-Francois, 1988. "A Representative Consumer Theory of the Logit Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(3), pages 461-466, August.
    8. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
    9. Nocke, Volker & Schutz, Nicolas, 2017. "Quasi-linear integrability," Journal of Economic Theory, Elsevier, vol. 169(C), pages 603-628.
    10. Alexander Konovalov & Zsolt Sándor, 2010. "On price equilibrium with multi-product firms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(2), pages 271-292, August.
    11. Ward Hanson & Kipp Martin, 1996. "Optimizing Multinomial Logit Profit Functions," Management Science, INFORMS, vol. 42(7), pages 992-1003, July.
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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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