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Equilibrium existence in price-quantity games: a sunk cost paradox

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Listed:
  • Iwan Bos

    (Maastricht University)

  • Dries Vermeulen

    (Maastricht University)

  • Niloufar Yousefimanesh

    (Maastricht University)

Abstract

Nonexistence of a pure-strategy Nash equilibrium is a notorious problem in price-quantity games. What drives this problem is the presence of spillover demand, i.e., demand coming from competitors’ unserved customers. We argue that such demand spillovers may stem from a strong implicit assumption that costs associated with obtaining a product are sunk and do not affect consumers’ future payoffs. We relax this assumption by considering a more general class of cost functions. This is shown to admit a pure-strategy equilibrium that coincides with the Bertrand price equilibrium.

Suggested Citation

  • Iwan Bos & Dries Vermeulen & Niloufar Yousefimanesh, 2025. "Equilibrium existence in price-quantity games: a sunk cost paradox," International Journal of Game Theory, Springer;Game Theory Society, vol. 54(2), pages 1-30, December.
    • Handle: RePEc:spr:jogath:v:54:y:2025:i:2:d:10.1007_s00182-025-00955-1
    DOI: 10.1007/s00182-025-00955-1
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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
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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