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Cournot–Bertrand comparison in a mixed oligopoly


  • Junichi Haraguchi
  • Toshihiro Matsumura


We revisit the classic discussion comparing price and quantity competition, but in a mixed oligopoly in which one state-owned public firm competes against private firms. It has been shown that in a mixed duopoly, price competition yields a larger profit for the private firm. This implies that firms face weaker competition under price competition, which contrasts sharply with the case of a private oligopoly. Here, we adopt a standard differentiated oligopoly with a linear demand. We find that regardless of the number of firms, price competition yields higher welfare. However, the profit ranking depends on the number of private firms. We find that if the number of private firms is greater than or equal to five, it is possible that quantity competition yields a larger profit for each private firm. We also endogenize the price-quantity choice. Here, we find that Bertrand competition can fail to be an equilibrium, unless there is only one private firm. Copyright Springer-Verlag Wien 2016

Suggested Citation

  • Junichi Haraguchi & Toshihiro Matsumura, 2016. "Cournot–Bertrand comparison in a mixed oligopoly," Journal of Economics, Springer, vol. 117(2), pages 117-136, March.
  • Handle: RePEc:kap:jeczfn:v:117:y:2016:i:2:p:117-136
    DOI: 10.1007/s00712-015-0452-6

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    Cited by:

    1. Susumu Sato & Toshihiro Matsumura, 2019. "Dynamic Privatization Policy," Manchester School, University of Manchester, vol. 87(1), pages 37-59, January.
    2. Leonard F. S. Wang & Arijit Mukherjee & Chenhang Zeng, 2020. "Does technology licensing matter for privatization?," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(5), pages 1462-1480, September.
    3. Haraguchi, Junichi & Matsumura, Toshihiro, 2018. "Government-leading welfare-improving collusion," International Review of Economics & Finance, Elsevier, vol. 56(C), pages 363-370.
    4. Junichi Haraguchi & Toshihiro Matsumura, 2020. "Optimal privatization policy with asymmetry among private firms," Bulletin of Economic Research, Wiley Blackwell, vol. 72(3), pages 213-224, July.
    5. Gutiérrez-Hita, Carlos & Vicente-Pérez, José, 2018. "On supply function competition in a mixed oligopoly," MPRA Paper 83792, University Library of Munich, Germany.
    6. Haraguchi, Junichi & Matsumura, Toshihiro & Yoshida, Shohei, 2018. "Competitive pressure from neighboring markets and optimal privatization policy," Japan and the World Economy, Elsevier, vol. 46(C), pages 1-8.
    7. Juan Carlos Bárcena-Ruiz & María Begoña Garzón, 0. "Partial privatization in an international mixed oligopoly under product differentiation," Journal of Economics, Springer, vol. 0, pages 1-24.
    8. Seung-Leul Kim & Sang-Ho Lee & Toshihiro Matsumura, 2019. "Corporate social responsibility and privatization policy in a mixed oligopoly," Journal of Economics, Springer, vol. 128(1), pages 67-89, September.
    9. Kosuke Hirose & Toshihiro Matsumura, 2019. "Comparing welfare and profit in quantity and price competition within Stackelberg mixed duopolies," Journal of Economics, Springer, vol. 126(1), pages 75-93, January.
    10. Ciprian Rusescu & Mihai Daniel Roman, 2020. "Product Differentiation Impact on Games Theory Models," Ovidius University Annals, Economic Sciences Series, Ovidius University of Constantza, Faculty of Economic Sciences, vol. 0(2), pages 500-508, December.
    11. Lee, Sang-Ho & Matsumura, Toshihiro & Sato, Susumu, 2017. "A New Approach to Free Entry Markets in Mixed Oligopolies: Welfare Implications," MPRA Paper 76450, University Library of Munich, Germany.
    12. Carlos, Gutiérrez-Hita & Vicente-Pérez, José, 2018. "On Supply Function Equilibria in a Mixed Duopoly," QM&ET Working Papers 18-1, University of Alicante, D. Quantitative Methods and Economic Theory.
    13. Toshihiro Matsumura & Akira Ogawa, 2017. "Endogenous Timing in Mixed Duopolies With Externality," Australian Economic Papers, Wiley Blackwell, vol. 56(4), pages 304-327, December.
    14. Junichi Haraguchi & Toshihiro Matsumura, 2020. "Endogenous public and private leadership with diverging social and private marginal costs," Manchester School, University of Manchester, vol. 88(5), pages 699-730, September.
    15. Duan, Lian, 2017. "Optimal degree of privatization in a mixed oligopoly with multiple public enterprises," MPRA Paper 82896, University Library of Munich, Germany.
    16. Xu, Lili & Chen, Yuyan & Lee, Sang-Ho, 2021. "Emission tax and strategic environmental corporate social responsibility in a Cournot–Bertrand comparison," MPRA Paper 108498, University Library of Munich, Germany.
    17. Kangsik Choi, 2019. "Price And Quantity Competition With Asymmetric Costs In A Mixed Duopoly: A Technical Note," Bulletin of Economic Research, Wiley Blackwell, vol. 71(1), pages 33-46, January.
    18. Hongkun Ma & X. Henry Wang & Chenhang Zeng, 2021. "Location choice and costly product differentiation in a mixed duopoly," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 66(1), pages 137-159, February.
    19. Chen, Jiaqi & Lee, Sang-Ho, 2021. "Cournot-Bertrand comparison under R&D competition: Output versus R&D subsidies," MPRA Paper 107949, University Library of Munich, Germany.

    More about this item


    Cournot; Bertrand; Mixed markets; Differentiated products; Oligopoly; H42; L13;
    All these keywords.

    JEL classification:

    • H42 - Public Economics - - Publicly Provided Goods - - - Publicly Provided Private Goods
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets


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