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Dynamic Cooperative Oligopolies

Author

Listed:
  • Ferenc Szidarovszky

    (Department of Mathematics, Corvinus University, Fövám tér 8, 1093 Budapest, Hungary)

  • Akio Matsumoto

    (Department of Economics, Chuo University, 742-1, Higashi-Nakano, Hachioji 192-0393, Japan)

Abstract

An n -person cooperative oligopoly is considered without product differentiation. It is assumed that the firms know the unit price function but have no access to the cost functions of the competitors. From market data, they have information about the industry output. The firms want to find the output levels that guarantee maximum industry profit. First, the existence of a unique maximizer is proven, which the firms cannot determine directly because of the lack of the knowledge of the cost functions. Instead, a dynamic model is constructed, which is asymptotically stable under realistic conditions, and the state trajectories converge to the optimum output levels of the firms. Three models are constructed: first, no time delay is assumed; second, information delay is considered for the firms on the industry output; and third, in addition, information delay is also assumed about the firms’ own output levels. The stability of the resulting no-delay, one-delay, and two-delay dynamics is examined.

Suggested Citation

  • Ferenc Szidarovszky & Akio Matsumoto, 2024. "Dynamic Cooperative Oligopolies," Mathematics, MDPI, vol. 12(6), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:891-:d:1358940
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    References listed on IDEAS

    as
    1. Saeed, Naima & Larsen, Odd I., 2010. "An application of cooperative game among container terminals of one port," European Journal of Operational Research, Elsevier, vol. 203(2), pages 393-403, June.
    2. Akio Matsumoto & Ferenc Szidarovszky, 2018. "Dynamic Oligopolies with Time Delays," Springer Books, Springer, number 978-981-13-1786-6, October.
    3. Furth, Dave, 1986. "Stability and instability in oligopoly," Journal of Economic Theory, Elsevier, vol. 40(2), pages 197-228, December.
    4. 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.
    5. Lemaire, Jean, 1991. "Cooperative Game Theory and its Insurance Applications," ASTIN Bulletin, Cambridge University Press, vol. 21(1), pages 17-40, April.
    Full references (including those not matched with items on IDEAS)

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