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Mixed Duopoly: Differential Game Approach

Author

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  • Koichi Futagami

    (Osaka University)

  • Toshihiro Matsumura

    (The University of Tokyo
    Osaka University)

  • Kizuku Takao

    (Aomori Public University)

Abstract

Previous studies in differential games reveal that intertemporal strategic behaviors have an important role for various economic problems. However, most of their analyses are limited to cases where objective functions are identical among agents. In this paper, we characterize the open-loop Nash equilibrium and the Markov perfect Nash equilibrium of a mixed duopoly game where a fully or partially state-owned firm and a fully private rm compete in the quantities of homogeneous goods with sticky prices. We show that in the Markov perfect Nash equilibrium, an increase in the governments' share-holdings of the state-owned firm has a non-monotonic effect on the price, and in a wide range of parameter spaces, it increases the price. These results are derived from the interaction of an asymmetric structure of agents' objectives and inter-temporal strategic behaviors, which are in sharp contrast with those in the open-loop Nash equilibrium. We provide new implications for privatization policies in the presence of dynamic interactions, against the static analyses.

Suggested Citation

  • Koichi Futagami & Toshihiro Matsumura & Kizuku Takao, 2017. "Mixed Duopoly: Differential Game Approach," KIER Working Papers 969, Kyoto University, Institute of Economic Research.
    • Handle: RePEc:kyo:wpaper:969
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    References listed on IDEAS

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    6. Matsumura, Toshihiro, 1998. "Partial privatization in mixed duopoly," Journal of Public Economics, Elsevier, vol. 70(3), pages 473-483, December.
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    Citations

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    Cited by:

    1. 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).
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    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

    Keywords

    Mixed Duopoly; Open-loop Nash equilibrium; Markov Perfect Nash equilibrium;
    All these keywords.

    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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