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Existence of Unique Equilibrium in Cournot Mixed Oligopoly

Author

Listed:
  • Koji Okuguchi

    (Tokyo Metropolitan University, Japan)

  • Takeshi Yamazaki

    (��Department of Economics, Niigata University, Japan)

Abstract

The properties of Cournot mixed oligopoly consisting of one public firm and one or more than one private firms have mostly been analyzed for simple cases on the basis of numerical calculations of the equilibrium values for a linear market demand function and linear or quadratic cost functions. In this paper, after proving the existence of a unique equilibrium in Cournot mixed oligopoly under general conditions on the market demand and each firm’s cost function, we derive conditions ensuring the existence of a unique Nash equilibrium for the mixed oligopoly where one public firm and at least one of the private firms are active in a general model of Cournot mixed oligopoly with one public firm and several private firms.

Suggested Citation

  • Koji Okuguchi & Takeshi Yamazaki, 2018. "Existence of Unique Equilibrium in Cournot Mixed Oligopoly," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-13, September.
    • Handle: RePEc:wsi:igtrxx:v:20:y:2018:i:03:n:s0219198917500359
    DOI: 10.1142/S0219198917500359
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    1. al-Nowaihi, A. & Levine, P. L., 1985. "The stability of the cournot oligopoly model: A reassessment," Journal of Economic Theory, Elsevier, vol. 35(2), pages 307-321, August.
    2. Lambertini, Luca & Mantovani, Andrea, 2014. "Feedback equilibria in a dynamic renewable resource oligopoly: Pre-emption, voracity and exhaustion," Journal of Economic Dynamics and Control, Elsevier, vol. 47(C), pages 115-122.
    3. Szidarovszky, F & Yakowitz, S, 1977. "A New Proof of the Existence and Uniqueness of the Cournot Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(3), pages 787-789, October.
    4. Charles D. Kolstad & Lars Mathiesen, 1987. "Necessary and Sufficient Conditions for Uniqueness of a Cournot Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(4), pages 681-690.
    5. Koji Okuguchi & Takeshi Yamazaki, 2004. "Stability Of Equilibrium In Bertrand And Cournot Duopolies," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 6(03), pages 381-390.
    6. K. Okuguchi, 1964. "The Stability of The Cournot Oligopoly Solution: A Further Generalization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 31(2), pages 143-146.
    7. Gérard Gaudet & Stephen W. Salant, 1991. "Uniqueness of Cournot Equilibrium: New Results From Old Methods," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(2), pages 399-404.
    8. Colombo, Luca & Labrecciosa, Paola, 2015. "On the Markovian efficiency of Bertrand and Cournot equilibria," Journal of Economic Theory, Elsevier, vol. 155(C), pages 332-358.
    9. Luca Grilli & Michele Bisceglia, 2017. "A Duopoly with Common Renewable Resource and Incentives," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-20, December.
    10. Seade, Jesus, 1980. "The stability of cournot revisited," Journal of Economic Theory, Elsevier, vol. 23(1), pages 15-27, August.
    11. Alex Possajennikov, 2003. "Imitation Dynamic and Nash Equilibrium in Cournot Oligopoly with Capacities," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 291-305.
    12. Koji Okuguchi & Takeshi Yamazaki, 2014. "Global Stability Of Nash Equilibrium In Aggregative Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1-15.
    13. repec:ebl:ecbull:v:12:y:2002:i:1:p:1-6 is not listed on IDEAS
    14. Koji Okuguchi, 2012. "General Analysis of Cournot Mixed Oligopoly with Partial Privatization," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 2(1), pages 48-62, June.
    15. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    16. Colombo, Luca & Labrecciosa, Paola, 2013. "On the convergence to the Cournot equilibrium in a productive asset oligopoly," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 441-445.
    17. Luca Lambertini, 2014. "Exploration For Nonrenewable Resources In A Dynamic Oligopoly: An Arrovian Result," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 1-11.
    18. Colombo, Luca & Labrecciosa, Paola, 2013. "Oligopoly exploitation of a private property productive asset," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 838-853.
    19. Shumei Hirai & Ferenc Szidarovszky, 2013. "Existence And Uniqueness Of Equilibrium In Asymmetric Contests With Endogenous Prizes," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-9.
    20. R. D. Theocharis, 1960. "On the Stability of the Cournot Solution on the Oligopoly Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 27(2), pages 133-134.
    21. Szidarovszky, Ferenc & Okuguchi, Koji, 1997. "On the Existence and Uniqueness of Pure Nash Equilibrium in Rent-Seeking Games," Games and Economic Behavior, Elsevier, vol. 18(1), pages 135-140, January.
    22. Matsumura, Toshihiro, 1998. "Partial privatization in mixed duopoly," Journal of Public Economics, Elsevier, vol. 70(3), pages 473-483, December.
    23. Toshihiro Matsumura & Osamu Kanda, 2005. "Mixed Oligopoly at Free Entry Markets," Journal of Economics, Springer, vol. 84(1), pages 27-48, February.
    24. Furth, Dave, 1986. "Stability and instability in oligopoly," Journal of Economic Theory, Elsevier, vol. 40(2), pages 197-228, December.
    25. F. H. Hahn, 1962. "The Stability of the Cournot Oligopoly Solution," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 29(4), pages 329-331.
    26. Gareth Myles, 2002. "Mixed oligopoly, subsidization and the order of firms' moves: an irrelevance result for the general case," Economics Bulletin, AccessEcon, vol. 12(1), pages 1-6.
    27. Okuguchi, Koji & Yamazaki, Takeshi, 2008. "Global stability of unique Nash equilibrium in Cournot oligopoly and rent-seeking game," Journal of Economic Dynamics and Control, Elsevier, vol. 32(4), pages 1204-1211, April.
    28. Takeshi Yamazaki, 2008. "On the Existence and Uniqueness of Pure‐Strategy Nash Equilibrium in Asymmetric Rent‐Seeking Contests," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(2), pages 317-327, April.
    29. Okuguchi, Koji, 1993. "Unified approach to Cournot models : Oligopoly, taxation and aggregate provision of a pure public good," European Journal of Political Economy, Elsevier, vol. 9(2), pages 233-245, May.
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    More about this item

    Keywords

    Mixed oligopoly; Cournot; equilibrium; existence;
    All these keywords.

    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • H32 - Public Economics - - Fiscal Policies and Behavior of Economic Agents - - - Firm

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