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On equivalence between Cournot competition and the Kreps–Scheinkman game


  • Wu, Xin-wang
  • Zhu, Quan-tao
  • Sun, Laixiang


The existing literature dealing with the equivalence between the Kreps–Scheinkman (KS) game and Cournot competition has focused on the case of a concave demand function. This paper analyzes the equivalence possibilities under the much extended circumstances of strictly decreasing marginal (industrial) revenue, a twice differentiable demand function, and convex costs. It proves that in the extended context, the outcomes in the subgame perfect Nash equilibrium (SPNE) of the KS game are those of Cournot equilibrium (CE) and that a CE is on the path of the SPNE of the KS game if the marginal cost of each firm in some special (borderline) cases is not too high. It further proves that for decreasing continuous demand and strictly increasing costs, the outcome in the SPNE of the KS game (if the SPNE exists) is that of CE. Based on these results, we argue that the KS game can serve as the basic form for studying “quantity competition” and for developing a T-stage game-theoretical framework to make competition form and timing endogenous.

Suggested Citation

  • Wu, Xin-wang & Zhu, Quan-tao & Sun, Laixiang, 2012. "On equivalence between Cournot competition and the Kreps–Scheinkman game," International Journal of Industrial Organization, Elsevier, vol. 30(1), pages 116-125.
  • Handle: RePEc:eee:indorg:v:30:y:2012:i:1:p:116-125 DOI: 10.1016/j.ijindorg.2011.07.002

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    References listed on IDEAS

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    Cited by:

    1. Carbonnier Cl´ement, 2014. "The incidence of non-linear consumption taxes," Научный результат. Серия «Экономические исследования», CyberLeninka;Федеральное государственное автономное образовательное учреждение высшего образования «Белгородский государственный национальный исследовательский университет», issue 1, pages 5-18.
    2. Carbonnier, Clément, 2014. "The incidence of non-linear price-dependent consumption taxes," Journal of Public Economics, Elsevier, vol. 118(C), pages 111-119.
    3. Barna Bakó & Attila Tasnádi, 2017. "The Kreps-Scheinkman Game in Mixed Duopolies," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 173(4), pages 753-768, December.
    4. Quan-tao Zhu & Xin-wang Wu & Laixiang Sun, 2014. "A generalized framework for endogenous timing in duopoly games and an application to price-quantity competition," Journal of Economics, Springer, vol. 112(2), pages 137-164, June.
    5. Tasnádi, Attila & Bakó, Barna, 2014. "A Kreps-Scheinkman-állítás érvényessége lineáris keresletű vegyes duopóliumok esetén
      [The Kreps and Scheinkman result remains valid for mixed duopolies with linear demand]
      ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(5), pages 533-543.
    6. Jacobs, Martin, 2016. "Number of firms, rationing, matching, and knowledge: A comprehensive study of variations in experimental Kreps-Scheinkman markets," Economics Working Papers 2016-02, Christian-Albrechts-University of Kiel, Department of Economics.

    More about this item


    Kreps–Scheinkman game; Quantity competition; Cournot competition; Efficient rationing rule;

    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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