Patterns of Competition with Captive Customers

Armstrong, Mark and Vickers, John (2018): Patterns of Competition with Captive Customers.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Oligopoly, Bertrand competition, Bertrand-Edgeworth competition, Consideration sets, Mixed strategies
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; D - Microeconomics > D4 - Market Structure, Pricing, and Design > D43 - Oligopoly and Other Forms of Market Imperfection; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D83 - Search ; Learning ; Information and Knowledge ; Communication ; Belief ; Unawareness; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L15 - Information and Product Quality ; Standardization and Compatibility

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