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Random Pricing: Bertrand Competition with Uncontested Consumers

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  • Severin Lenhard

    (Universität St. Gallen
    Secretariat of the Swiss Competition Commission)

Abstract

Two firms offer a homogeneous product and compete in prices. Consumers are homogeneous yet differ in their access to the firms. Three groups exist: Consumers who have access to both firms and can compare prices; and consumers who can access only one of the two firms and are thus uncontested. The group sizes may differ: One firm’s uncontested consumer base may be zero. No pure strategy equilibrium exists. In the mixed equilibrium, firms randomize on the same continuum of prices; in expectation, the firm with the larger consumer base plays a higher price and has a higher expected demand. We study: the firms’ incentive to invest in demand; effects of price discrimination; and collusion. Moreover, we extend the model to more than two firms and discuss mergers.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:revind:v:67:y:2025:i:2:d:10.1007_s11151-025-10013-5
    DOI: 10.1007/s11151-025-10013-5
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    Keywords

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    JEL classification:

    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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