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Patterns of Competitive Interaction

Author

Listed:
  • Mark Armstrong
  • John Vickers

Abstract

We explore patterns of price competition in an oligopoly where consumers vary in the set of firms they consider for their purchase and buy from the lowest-priced firm they consider. We study a pattern of consideration, termed "symmetric interactions", that generalises models used in existing work (duopoly, symmetric firms, and firms with independent reach). Within this class, equilibrium profits are proportional to a firm's reach, firms with a larger reach set higher average prices, and a reduction in the number of firms (either by exit or by merger) harms consumers. However, increased competition (either by entry of by increased consumer awareness) does not always benefit consumers. We go on to study patterns of consideration with asymmetric interactions. In situations with disjoint reach and with nested reach we find equilibria in which price competition is "duopolistic": only two firms compete within each price range. We characterize the contrasting equilibrium patterns of price competition for all patterns of consideration in the three-firm case.

Suggested Citation

  • Mark Armstrong & John Vickers, 2021. "Patterns of Competitive Interaction," Economics Series Working Papers 936, University of Oxford, Department of Economics.
    • Handle: RePEc:oxf:wpaper:936
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    2. Mark Armstrong & John Vickers, 2023. "Multibrand Price Dispersion," Economics Series Working Papers 1029, University of Oxford, Department of Economics.
    3. Christian Oertel & Armin Schmutzler, 2022. "Challenging the incumbent: Entry in markets with captive consumers and taste heterogeneity," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 31(4), pages 961-979, November.
    4. Kishishita, Daiki & Sato, Susumu, 2025. "Watchdog versus yes man: News source and media competition," Games and Economic Behavior, Elsevier, vol. 153(C), pages 233-253.
    5. 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.
    6. Vickers, John, 2021. "Competition for imperfect consumers," International Journal of Industrial Organization, Elsevier, vol. 79(C).
    7. Chioveanu, Ioana, 2024. "Consumer data and price discrimination by consideration sets," Economics Letters, Elsevier, vol. 236(C).
    8. Heski Bar-Isaac & Sandro Shelegia, 2023. "Search, Showrooming, and Retailer Variety," Marketing Science, INFORMS, vol. 42(2), pages 251-270, March.
    9. Rafael R. Guthmann, 2025. "Imperfect Competition as a Result of Unawareness," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 67(1), pages 35-53, June.
    10. Jelovac, Izabela, 2026. "Generic entry, price competition, and market segmentation in the prescription drug market – a comment," International Journal of Industrial Organization, Elsevier, vol. 104(C).
    11. Rafael R. Guthmann, 2024. "Price dispersion in dynamic competition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(4), pages 1203-1232, December.
    12. Severin Lenhard, 2025. "Random Pricing: Bertrand Competition with Uncontested Consumers," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 67(2), pages 191-208, August.
    13. Saur, Marc P. & Schlatterer, Markus G. & Schmitt, Stefanie Y., 2022. "Limited perception and price discrimination in a model of horizontal product differentiation," Games and Economic Behavior, Elsevier, vol. 134(C), pages 151-168.
    14. Gehrig, Thomas & Ritzberger, Klaus, 2022. "Intermediation and price volatility," Journal of Economic Theory, Elsevier, vol. 201(C).

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    Keywords

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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