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On equivalence between Cournot competition and the Kreps–Scheinkman game

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

Abstract

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.

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Bibliographic Info

Article provided by Elsevier in its journal International Journal of Industrial Organization.

Volume (Year): 30 (2012)
Issue (Month): 1 ()
Pages: 116-125

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Handle: RePEc:eee:indorg:v:30:y:2012:i:1:p:116-125

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Web page: http://www.elsevier.com/locate/inca/505551

Related research

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

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References

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  1. Cheng-Zhong Qin & Charles Stuart, 1997. "Bertrand versus Cournot revisited," Economic Theory, Springer, vol. 10(3), pages 497-507.
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Citations

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Cited by:
  1. 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.
  2. Bakó, Barna & Tasnádi, Attila, 2014. "The Kreps-Scheinkman game in mixed duopolies," MPRA Paper 52986, University Library of Munich, Germany.
  3. Clément Carbonnier, 2013. "The Incidence of Non-Linear Consumption Taxes," THEMA Working Papers 2013-19, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.

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