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On Stochastic Variational Inequalities with Mean Value Constraints

Author

Listed:
  • Francesca Faraci

    (Università di Catania)

  • Baasansuren Jadamba

    (Rochester Institute of Technology)

  • Fabio Raciti

    (Università di Catania)

Abstract

In this note, we consider a class of variational inequalities on probabilistic Lebesgue spaces, where the constraints are satisfied on average, and provide an approximation procedure for the solutions. As an application, we investigate the Nash–Cournot oligopoly problem with uncertain data and compare the solutions obtained when the constraints are satisfied on average with the ones obtained when the constraints are satisfied almost surely.

Suggested Citation

  • Francesca Faraci & Baasansuren Jadamba & Fabio Raciti, 2016. "On Stochastic Variational Inequalities with Mean Value Constraints," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 675-693, November.
    • Handle: RePEc:spr:joptap:v:171:y:2016:i:2:d:10.1007_s10957-016-0888-z
    DOI: 10.1007/s10957-016-0888-z
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    References listed on IDEAS

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    1. Joachim Gwinner & Fabio Raciti, 2012. "Some equilibrium problems under uncertainty and random variational inequalities," Annals of Operations Research, Springer, vol. 200(1), pages 299-319, November.
    2. Shu Lu & Amarjit Budhiraja, 2013. "Confidence Regions for Stochastic Variational Inequalities," Mathematics of Operations Research, INFORMS, vol. 38(3), pages 545-568, August.
    3. Bonenti, Francesca & Oggioni, Giorgia & Allevi, Elisabetta & Marangoni, Giacomo, 2013. "Evaluating the EU ETS impacts on profits, investments and prices of the Italian electricity market," Energy Policy, Elsevier, vol. 59(C), pages 242-256.
    4. Xiaojun Chen & Masao Fukushima, 2005. "Expected Residual Minimization Method for Stochastic Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 1022-1038, November.
    5. Baasansuren Jadamba & Fabio Raciti, 2015. "On the Modeling of Some Environmental Games with Uncertain Data," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 959-968, December.
    6. B. Jadamba & F. Raciti, 2015. "Variational Inequality Approach to Stochastic Nash Equilibrium Problems with an Application to Cournot Oligopoly," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 1050-1070, June.
    7. Patrizia Daniele & Sofia Giuffrè, 2015. "Random Variational Inequalities and the Random Traffic Equilibrium Problem," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 363-381, October.
    8. 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.
    9. Patriksson, Michael, 2008. "On the applicability and solution of bilevel optimization models in transportation science: A study on the existence, stability and computation of optimal solutions to stochastic mathematical programs," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 843-860, December.
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    Cited by:

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