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Mixed duopoly: Differential game approach


  • Koichi Futagami
  • Toshihiro Matsumura
  • Kizuku Takao


This study formulates a dynamic mixed oligopoly model, in which a state‐owned public firm competes against a private firm over multiple periods. We adopt a differential game formulated by Fershtman and Kamien [Econometrica 55 (1987), pp. 1151–1164] and investigate how the dynamic competition affects the optimal privatization policy. We characterize the open‐loop Nash equilibrium (OLNE) and Markov‐perfect Nash equilibrium (MPNE). We show that in the MPNE, an increase in the degree of privatization has a nonmonotonic effect on the price, increasing it in a wide range of parameter spaces, which is in sharp contrast to the result in the OLNE or static analyses. We also find that the optimal degree of privatization is higher in the MPNE than that in the OLNE and static equilibrium. These results suggest that intertemporal strategic behavior changes the optimal privatization policy.

Suggested Citation

  • Koichi Futagami & Toshihiro Matsumura & Kizuku Takao, 2019. "Mixed duopoly: Differential game approach," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 21(4), pages 771-793, August.
  • Handle: RePEc:bla:jpbect:v:21:y:2019:i:4:p:771-793
    DOI: 10.1111/jpet.12372

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    References listed on IDEAS

    1. Benhabib Jess & Perli Roberto, 1994. "Uniqueness and Indeterminacy: On the Dynamics of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 63(1), pages 113-142, June.
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    6. Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-1164, September.
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    Cited by:

    1. Fan Zhang & Susu Cheng, 2021. "Behavioral choices in a dynamic duopoly with process innovation and sticky price: Myopia versus farsightedness," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 42(3), pages 662-674, April.
    2. Mukherjee, Arka & Carvalho, Margarida, 2021. "Dynamic decision making in a mixed market under cooperation: Towards sustainability," International Journal of Production Economics, Elsevier, vol. 241(C).
    3. Pu‐yan Nie & Yong‐cong Yang, 2020. "Cost‐reduction innovation under mixed economy," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 41(7), pages 1195-1201, October.
    4. Marc Escrihuela‐Villar & Carlos Gutiérrez‐Hita & José Vicente‐Pérez, 2020. "Supply function competition in a mixed electric power market," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(4), pages 1151-1175, August.
    5. Yi Liu & Leonard F.S. Wang & Chenhang Zeng, 2023. "Upstream privatization and downstream licensing," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(1), pages 148-165, March.
    6. Yi Liu & Toshihiro Matsumura & Chenhang Zeng, 2021. "The relationship between privatization and corporate taxation policies," Journal of Economics, Springer, vol. 133(1), pages 85-101, June.
    7. Haraguchi, Junichi & Matsumura, Toshihiro, 2020. "Common Ownership among Private Firms and Privatization Policies," MPRA Paper 102152, University Library of Munich, Germany.
    8. Xia Wang & Tingting Tan & Mingqing Xing, 2022. "Environmental awareness of the private firm and optimal privatization in a mixed duopoly," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(8), pages 4055-4063, December.
    9. Okuyama, Suzuka, 2021. "Price and quality competition in a mixed duopoly : Differential game approach," MPRA Paper 110148, University Library of Munich, Germany, revised 06 Oct 2021.

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    More about this item

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L32 - Industrial Organization - - Nonprofit Organizations and Public Enterprise - - - Public Enterprises; Public-Private Enterprises


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