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A random time-dependent noncooperative equilibrium problem

Author

Listed:
  • Annamaria Barbagallo

    (University of Naples Federico II)

  • Serena Guarino Lo Bianco

    (University of Naples Federico II)

Abstract

The paper deals with the random time-dependent oligopolistic market equilibrium problem. For such a problem the firms’ point of view has been analyzed in Barbagallo and Guarino Lo Bianco (Optim. Lett. 14: 2479–2493, 2020) while here the policymaker’s point of view is studied. The random dynamic optimal control equilibrium conditions are expressed by means of an inverse stochastic time-dependent variational inequality which is proved to be equivalent to a stochastic time-dependent variational inequality. Some existence and well-posedness results for optimal regulatory taxes are obtained. Moreover a numerical scheme to compute the solution to the stochastic time-dependent variational inequality is presented. Finally an example is discussed.

Suggested Citation

  • Annamaria Barbagallo & Serena Guarino Lo Bianco, 2023. "A random time-dependent noncooperative equilibrium problem," Computational Optimization and Applications, Springer, vol. 84(1), pages 27-52, January.
    • Handle: RePEc:spr:coopap:v:84:y:2023:i:1:d:10.1007_s10589-022-00368-w
    DOI: 10.1007/s10589-022-00368-w
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    References listed on IDEAS

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    1. Alfredo N. Iusem & Alejandro Jofré & Philip Thompson, 2019. "Incremental Constraint Projection Methods for Monotone Stochastic Variational Inequalities," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 236-263, February.
    2. Annamaria Barbagallo & Paolo Mauro, 2012. "Time-Dependent Variational Inequality for an Oligopolistic Market Equilibrium Problem with Production and Demand Excesses," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-35, July.
    3. Aswin Kannan & Uday V. Shanbhag, 2019. "Optimal stochastic extragradient schemes for pseudomonotone stochastic variational inequality problems and their variants," Computational Optimization and Applications, Springer, vol. 74(3), pages 779-820, December.
    4. Annamaria Barbagallo & Paolo Mauro, 2012. "Evolutionary Variational Formulation for Oligopolistic Market Equilibrium Problems with Production Excesses," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 288-314, October.
    5. Annamaria Barbagallo & Serena Guarino Lo Bianco, 2020. "On ill-posedness and stability of tensor variational inequalities: application to an economic equilibrium," Journal of Global Optimization, Springer, vol. 77(1), pages 125-141, May.
    6. Rachel Hawks & Baasansuren Jadamba & Akhtar A. Khan & Miguel Sama & Yidan Yang, 2021. "A Variational Inequality Based Stochastic Approximation for Inverse Problems in Stochastic Partial Differential Equations," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Panos M. Pardalos (ed.), Nonlinear Analysis and Global Optimization, pages 207-226, Springer.
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