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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.

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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    1. Carl Davidson & Raymond Deneckere, 1986. "Long-Run Competition in Capacity, Short-Run Competition in Price, and the Cournot Model," RAND Journal of Economics, The RAND Corporation, vol. 17(3), pages 404-415, Autumn.
    2. Hamilton, Jonathan H. & Slutsky, Steven M., 1990. "Endogenous timing in duopoly games: Stackelberg or cournot equilibria," Games and Economic Behavior, Elsevier, vol. 2(1), pages 29-46, March.
    3. Paul Madden, 1998. "Elastic demand, sunk costs and the Kreps-Scheinkman extension of the Cournot model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(1), pages 199-212.
    4. Dan Kovenock & Raymond J. Deneckere, 1996. "Bertrand-Edgeworth duopoly with unit cost asymmetry (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 1-25.
    5. Billette de Villemeur, Etienne & Vinella, Annalisa, 2011. "Long-term contracting in hydro-thermal electricity generation: Welfare and environmental impact," Utilities Policy, Elsevier, vol. 19(1), pages 20-32, January.
    6. Irwin, Douglas A. & Pavcnik, Nina, 2004. "Airbus versus Boeing revisited: international competition in the aircraft market," Journal of International Economics, Elsevier, vol. 64(2), pages 223-245, December.
    7. Cheng-Zhong Qin & Charles Stuart, 1997. "Bertrand versus Cournot revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(3), pages 497-507.
    8. Robson, Arthur J, 1990. "Duopoly with Endogenous Strategic Timing: Stackelberg Regained," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(2), pages 263-274, May.
    9. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 27-41.
    10. Lepore Jason J, 2009. "Consumer Rationing and the Cournot Outcome," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-46, September.
    11. Paul Krugman & Alasdair Smith, 1994. "Empirical Studies of Strategic Trade Policy," NBER Books, National Bureau of Economic Research, Inc, number krug94-1.
    12. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, December.
    13. Gernot Klepper, 1994. "Industrial Policy in the Transport Aircraft Industry," NBER Chapters, in: Empirical Studies of Strategic Trade Policy, pages 101-130, National Bureau of Economic Research, Inc.
    14. Lepore, Jason J., 2008. "Cournot and Bertrand-Edgeworth competition when rivals' costs are unknown," Economics Letters, Elsevier, vol. 101(3), pages 237-240, December.
    15. Nicolas Gruyer, 2009. "A note on quantity precommitment, cournot outcome and asymmetric capacity costs," Economics Bulletin, AccessEcon, vol. 29(1), pages 384-391.
    16. Klepper, Gernot, 1990. "Entry into the market for large transport aircraft," European Economic Review, Elsevier, vol. 34(4), pages 775-798, June.
    17. Nicolas Gruyer, 2009. "A note on quantity precommitment, Cournot outcome and asymmetric capacity costs," Post-Print hal-01021567, HAL.
    18. Crampes, C. & Moreaux, M., 2001. "Water resource and power generation," International Journal of Industrial Organization, Elsevier, vol. 19(6), pages 975-997, May.
    19. Dastidar, Krishnendu Ghosh, 2004. "On Stackelberg games in a homogeneous product market," European Economic Review, Elsevier, vol. 48(3), pages 549-562, June.
    20. David M. Kreps & Jose A. Scheinkman, 1983. "Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 326-337, Autumn.
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    Cited by:

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    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. Carbonnier, Clément, 2014. "The incidence of non-linear price-dependent consumption taxes," Journal of Public Economics, Elsevier, vol. 118(C), pages 111-119.
    7. 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.

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    More about this item

    Keywords

    Kreps–Scheinkman game; Quantity competition; Cournot competition; Efficient rationing rule;
    All these keywords.

    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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