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Patterns of Competition with Captive Customers

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  • Armstrong, Mark
  • Vickers, John

Abstract

We study mixed-strategy equilibrium pricing in oligopoly settings where consumers vary in the set of suppliers they consider for their purchase---some being captive to a particular firm, some consider two particular firms, and so on. In the case of "nested reach" we find equilibria, unlike those in more standard models, in which firms are ranked in terms of the prices they might charge. We characterize equilibria in the three-firm case, and contrast them with equilibria in the parallel model with capacity constraints. A theme of the analysis is how patterns of consumer interaction with firms matter for competitive outcomes.

Suggested Citation

  • Armstrong, Mark & Vickers, John, 2018. "Patterns of Competition with Captive Customers," MPRA Paper 90362, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:90362
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    References listed on IDEAS

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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. Foucart, Renaud & Friedrichsen, Jana, 2021. "All-pay competition with captive consumers," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics.
    3. Mark Armstrong & John Vickers, 2022. "Patterns of Competitive Interaction," Econometrica, Econometric Society, vol. 90(1), pages 153-191, January.
    4. Salvadori, Neri & De Francesco, Massimo A., 2020. "Bertrand-Edgeworth oligopoly: Characterization of mixed strategy equilibria when some firms are large and the others are small," MPRA Paper 102274, University Library of Munich, Germany.

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    More about this item

    Keywords

    Oligopoly; Bertrand competition; Bertrand-Edgeworth competition; Consideration sets; Mixed strategies;
    All these keywords.

    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
    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance
    • L15 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Information and Product Quality

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