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Mixed Duopoly: Differential Game Approach

Author

Listed:
  • Koichi Futagami

    () (Graduate School of Economics, Osaka University)

  • Toshihiro Matsumura

    () (Institute of Social Science, The University of Tokyo)

  • Kizuku Takao

    () (Department of Economics, 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 firm compete in the quantities of homogeneous goods with sticky prices. We show that in the Markov perfect Nash equilibrium, an increase in the governments f 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 f objectives and inter-temporal strategic behaviors, which are in sharp contrast with those in the open-loop Nash equilibrium. We provide new implications for privatizationpolicies in the presence of dynamic interactions, against the static analyses.

Suggested Citation

  • Koichi Futagami & Toshihiro Matsumura & Kizuku Takao, 2017. "Mixed Duopoly: Differential Game Approach," Discussion Papers in Economics and Business 17-03, Osaka University, Graduate School of Economics.
  • Handle: RePEc:osk:wpaper:1703
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    References listed on IDEAS

    as
    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.
    2. Tsutsui, Shunichi & Mino, Kazuo, 1990. "Nonlinear strategies in dynamic duopolistic competition with sticky prices," Journal of Economic Theory, Elsevier, vol. 52(1), pages 136-161, October.
    3. Trimborn, Timo & Koch, Karl-Josef & Steger, Thomas M., 2008. "Multidimensional Transitional Dynamics: A Simple Numerical Procedure," Macroeconomic Dynamics, Cambridge University Press, vol. 12(03), pages 301-319, June.
    4. Stefano Colombo, 2016. "Mixed oligopolies and collusion," Journal of Economics, Springer, vol. 118(2), pages 167-184, June.
    5. Piga, Claudio A. G., 2000. "Competition in a duopoly with sticky price and advertising," International Journal of Industrial Organization, Elsevier, vol. 18(4), pages 595-614, May.
    6. Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-1164, September.
    7. Toshihiro Matsumura & Osamu Kanda, 2005. "Mixed Oligopoly at Free Entry Markets," Journal of Economics, Springer, vol. 84(1), pages 27-48, February.
    8. Cabral, Luís, 2012. "Oligopoly Dynamics," International Journal of Industrial Organization, Elsevier, vol. 30(3), pages 278-282.
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    More about this item

    Keywords

    Mixed Duopoly; Open-loop Nash equilibrium; Markov Perfect Nash equilibrium;

    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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