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The only Dance in Town: Unique Equilibrium in a Generalized Model of Price Competition

Author

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  • Johnen, Johannes

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

  • Ronayne, David

Abstract

We study a canonical model of simultaneous price competition between firms that sell a homogeneous good to consumers who are characterized by the number of prices they are exogenously aware of. Our setting subsumes many employed in the literature over the last several decades. We show there is a unique equilibrium if and only if there exist some consumers who are aware of exactly two prices. The equilibrium we derive is in symmetric mixed strategies. Furthermore, when there are no consumers aware of exactly two prices, we show there is an uncountable-infinity of asymmetric equilibria in addition to the symmetric equilibrium. Our results show the paradigm generically produces a unique equilibrium. We also show that the commonly-sought symmetric equilibrium (which also nests the textbook Bertrand pure strategy equilibrium as a special case) is robust to perturbations in consumer behavior, while the asymmetric equilibria are not.

Suggested Citation

  • Johnen, Johannes & Ronayne, David, 2021. "The only Dance in Town: Unique Equilibrium in a Generalized Model of Price Competition," LIDAM Reprints CORE 3187, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:3187
    DOI: https://doi.org/10.1111/joie.12264
    Note: In: The Journal of Industrial Economics, 2021, vol. 69(3), p. 595-614
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    Cited by:

    1. Armstrong, Mark & Vickers, John, 2020. "Patterns of Price Competition and the Structure of Consumer Choice," MPRA Paper 98346, University Library of Munich, Germany.
    2. David Ronayne, 2021. "Price Comparison Websites," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(3), pages 1081-1110, August.
    3. Atayev, Atabek, 2022. "Uncertain product availability in search markets," Journal of Economic Theory, Elsevier, vol. 204(C).
    4. Mark Armstrong & John Vickers, 2022. "Patterns of Competitive Interaction," Econometrica, Econometric Society, vol. 90(1), pages 153-191, January.
    5. David P. Myatt & David Ronayne, 2023. "Asymmetric Models of Sales," Rationality and Competition Discussion Paper Series 450, CRC TRR 190 Rationality and Competition.
    6. David Ronayne & Greg Taylor, 2022. "Competing Sales Channels with Captive Consumers," The Economic Journal, Royal Economic Society, vol. 132(642), pages 741-766.

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