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

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  • Johannes Johnen
  • David Ronayne

Abstract

We study a model of simultaneous price competition that subsumes many employed in the literature over the last several decades. Firms sell a homogeneous good to consumers characterized by the number of prices they (exogenously) consider. We show there is a unique equilibrium if and only if some consumers consider exactly two prices. The equilibrium is in symmetric mixed strategies. When no consumer considers exactly two prices, there is, in addition, an uncountable infinity of asymmetric equilibria. Our results show that the paradigm generically produces a unique equilibrium, and only the commonly sought symmetric equilibrium is robust to perturbations in consumer behavior.

Suggested Citation

  • Johannes Johnen & David Ronayne, 2021. "The only Dance in Town: Unique Equilibrium in a Generalized Model of Price Competition," Journal of Industrial Economics, Wiley Blackwell, vol. 69(3), pages 595-614, September.
  • Handle: RePEc:bla:jindec:v:69:y:2021:i:3:p:595-614
    DOI: 10.1111/joie.12264
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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. Chioveanu, Ioana, 2024. "Consumer data and price discrimination by consideration sets," Economics Letters, Elsevier, vol. 236(C).
    7. 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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