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On computation of optimal strategies in oligopolistic markets respecting the cost of change

Author

Listed:
  • Jiří V. Outrata

    (Czech Academy of Sciences
    Federation University of Australia)

  • Jan Valdman

    (Czech Academy of Sciences
    University of South Bohemia)

Abstract

The paper deals with a class of parameterized equilibrium problems, where the objectives of the players do possess nonsmooth terms. The respective Nash equilibria can be characterized via a parameter-dependent variational inequality of the second kind, whose Lipschitzian stability, under appropriate conditions, is established. This theory is then applied to evolution of an oligopolistic market in which the firms adapt their production strategies to changing input costs, while each change of the production is associated with some “costs of change”. We examine both the Cournot-Nash equilibria as well as the two-level case, when one firm decides to take over the role of the Leader (Stackelberg equilibrium). The impact of costs of change is illustrated by academic examples.

Suggested Citation

  • Jiří V. Outrata & Jan Valdman, 2020. "On computation of optimal strategies in oligopolistic markets respecting the cost of change," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(3), pages 489-509, December.
    • Handle: RePEc:spr:mathme:v:92:y:2020:i:3:d:10.1007_s00186-020-00721-x
    DOI: 10.1007/s00186-020-00721-x
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    References listed on IDEAS

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    1. Nicola Basilico & Stefano Coniglio & Nicola Gatti & Alberto Marchesi, 2020. "Bilevel programming methods for computing single-leader-multi-follower equilibria in normal-form and polymatrix games," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(1), pages 3-31, March.
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    Cited by:

    1. Zhen-Ping Yang & Gui-Hua Lin, 2021. "Variance-Based Single-Call Proximal Extragradient Algorithms for Stochastic Mixed Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 393-427, August.

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