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On pure-strategy Nash equilibria in price–quantity games

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  • Bos, Iwan
  • Vermeulen, Dries

Abstract

This paper examines the existence and characteristics of pure-strategy Nash equilibria in oligopoly models in which firms simultaneously set prices and quantities. Existence of a pure-strategy equilibrium is proved for a class of price–quantity games. If the demand function is continuous, then the equilibrium outcome is similar to that of a price-only model. With discontinuous demand and limited spillover, there are rationing equilibria in which combined production falls short of market demand. Moreover, there might again be an equilibrium reflecting the outcome of a price game. Competition in price and quantity thus yields Bertrand outcomes under a variety of market conditions.

Suggested Citation

  • Bos, Iwan & Vermeulen, Dries, 2021. "On pure-strategy Nash equilibria in price–quantity games," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    • Handle: RePEc:eee:mateco:v:96:y:2021:i:c:s0304406821000392
    DOI: 10.1016/j.jmateco.2021.102501
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    Cited by:

    1. Bos, Iwan & Vermeulen, Dries, 2021. "Equilibrium existence with spillover demand," Economics Letters, Elsevier, vol. 208(C).
    2. R. A. Edwards & R. R. Routledge, 2023. "Existence and uniqueness of Nash equilibrium in discontinuous Bertrand games: a complete characterization," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(2), pages 569-586, June.
    3. Iwan Bos & Marco A. Marini, 2022. "Oligopoly Pricing: The Role of Firm Size and Number," Games, MDPI, vol. 14(1), pages 1-16, December.
    4. Edwards, Robert A. & Routledge, Robert R., 2022. "Information, Bertrand–Edgeworth competition and the law of one price," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    5. Tasnádi, Attila, 2020. "Production in advance versus production to order: Equilibrium and social surplus," Mathematical Social Sciences, Elsevier, vol. 106(C), pages 11-18.
    6. Yousefimanesh, Niloofar & Bos, Iwan & Vermeulen, Dries, 2023. "Strategic rationing in Stackelberg games," Games and Economic Behavior, Elsevier, vol. 140(C), pages 529-555.
    7. Mongoljin Batsaikhan & Norovsambuu Tumennasan, 2018. "Output Decisions and Price Matching: Theory and Experiment," Management Science, INFORMS, vol. 64(8), pages 3609-3624, August.

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