IDEAS home Printed from https://ideas.repec.org/a/eee/indorg/v30y2012i1p116-125.html
   My bibliography  Save this article

On equivalence between Cournot competition and the Kreps–Scheinkman game

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016771871100066X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ijindorg.2011.07.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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, March.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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.
    4. 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.
    5. Carbonnier, Clément, 2014. "The incidence of non-linear price-dependent consumption taxes," Journal of Public Economics, Elsevier, vol. 118(C), pages 111-119.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Pedro Jara-Moroni, 2008. "The Cournot outcome as the result of price competition," PSE Working Papers halshs-00587866, HAL.
    3. 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.
    4. Attila Tasnádi, 2010. "Quantity-setting games with a dominant firm," Journal of Economics, Springer, vol. 99(3), pages 251-266, April.
    5. Lepore, Jason J., 2012. "Cournot outcomes under Bertrand–Edgeworth competition with demand uncertainty," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 177-186.
    6. Jason J. Lepore & Aric P. Shafran, 2013. "Consumer Rationing and Cournot Outcomes: Experimental Evidence," Southern Economic Journal, John Wiley & Sons, vol. 79(3), pages 727-746, January.
    7. Luca Lambertini, 2000. "Strategic Delegation and the Shape of Market Competition," Scottish Journal of Political Economy, Scottish Economic Society, vol. 47(5), pages 550-570, November.
    8. Allison, Blake A. & Lepore, Jason J., 2014. "Verifying payoff security in the mixed extension of discontinuous games," Journal of Economic Theory, Elsevier, vol. 152(C), pages 291-303.
    9. Massimo A. Francesco, 2014. "A Dynamic Entry And Price Game With Capacity Indivisibility," Bulletin of Economic Research, Wiley Blackwell, vol. 66(4), pages 406-419, October.
    10. 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.
    11. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2020. "A general model of price competition with soft capacity constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(1), pages 95-120, July.
    12. Attila Tasnádi, 2016. "Endogenous timing of moves in Bertrand–Edgeworth triopolies," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(4), pages 317-334, December.
    13. Vettas, Nikolaos & Biglaiser, Gary, 2004. "Dynamic Price Competition with Capacity Constraints and Strategic Buyers," CEPR Discussion Papers 4315, C.E.P.R. Discussion Papers.
    14. Jean J. Gabszewicz & Jacques-François Thisse, 2000. "Microeconomic theories of imperfect competition," Cahiers d'Économie Politique, Programme National Persée, vol. 37(1), pages 47-99.
    15. Tasnádi, Attila, 2001. "A Bertrand-Edgeworth-oligopóliumok. Irodalmi áttekintés [Bertrand-Edgeworth oligopolies - a survey of the literature]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(12), pages 1081-1092.
    16. Roy Chowdhury, Prabal, 2008. "Bertrand-Edgeworth equilibrium with a large number of firms," International Journal of Industrial Organization, Elsevier, vol. 26(3), pages 746-761, May.
    17. De Francesco, Massimo A. & Salvadori, Neri, 2023. "Bertrand-Edgeworth game under oligopoly. General results and comparisons with duopoly," MPRA Paper 118237, University Library of Munich, Germany.
    18. De Francesco, Massimo A. & Salvadori, Neri, 2016. "Bertrand-Edgeworth games under triopoly: the equilibrium strategies when the payoffs of the two smallest firms are proportional to their capacities," MPRA Paper 69999, University Library of Munich, Germany.
    19. Severin Lenhard, 2021. "Imperfect Competition with Costly Disposal," Diskussionsschriften dp2105, Universitaet Bern, Departement Volkswirtschaft.
    20. Arnott, Richard & Rowse, John, 2009. "Downtown parking in auto city," Regional Science and Urban Economics, Elsevier, vol. 39(1), pages 1-14, January.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:indorg:v:30:y:2012:i:1:p:116-125. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505551 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.