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On Distributionally Robust Generalized Nash Games Defined over the Wasserstein Ball

Author

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  • Filippo Fabiani

    (IMT School for Advanced Studies Lucca)

  • Barbara Franci

    (Maastricht University)

Abstract

In this paper we propose an exact, deterministic, and fully continuous reformulation of generalized Nash games characterized by the presence of soft coupling constraints in the form of distributionally robust (DR) joint chance-constraints (CCs). We first rewrite the underlying uncertain game introducing mixed-integer variables to cope with DR–CCs, where the integer restriction actually amounts to a binary decision vector only, and then extend it to an equivalent deterministic problem with one additional agent handling all those introduced variables. Successively we show that, by means of a careful choice of tailored penalty functions, the extended deterministic game with additional agent can be equivalently recast in a fully continuous setting.

Suggested Citation

  • Filippo Fabiani & Barbara Franci, 2023. "On Distributionally Robust Generalized Nash Games Defined over the Wasserstein Ball," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 298-309, October.
    • Handle: RePEc:spr:joptap:v:199:y:2023:i:1:d:10.1007_s10957-023-02284-3
    DOI: 10.1007/s10957-023-02284-3
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    References listed on IDEAS

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    1. R. Myerson, 2010. "Nash Equilibrium and the History of Economic Theory," Voprosy Ekonomiki, NP Voprosy Ekonomiki, issue 6.
    2. Drazen Prelec & George Loewenstein, 1991. "Decision Making Over Time and Under Uncertainty: A Common Approach," Management Science, INFORMS, vol. 37(7), pages 770-786, July.
    3. M. Raghavachari, 1969. "On Connections Between Zero-One Integer Programming and Concave Programming Under Linear Constraints," Operations Research, INFORMS, vol. 17(4), pages 680-684, August.
    4. Hoang Nam Nguyen & Abdel Lisser & Vikas Vikram Singh, 2022. "Random Games Under Elliptically Distributed Dependent Joint Chance Constraints," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 249-264, October.
    5. Wildasin, David E., 1988. "Nash equilibria in models of fiscal competition," Journal of Public Economics, Elsevier, vol. 35(2), pages 229-240, March.
    6. Wolfram Wiesemann & Daniel Kuhn & Melvyn Sim, 2014. "Distributionally Robust Convex Optimization," Operations Research, INFORMS, vol. 62(6), pages 1358-1376, December.
    7. Yu Zhang & Zhenzhen Zhang & Andrew Lim & Melvyn Sim, 2021. "Robust Data-Driven Vehicle Routing with Time Windows," Operations Research, INFORMS, vol. 69(2), pages 469-485, March.
    8. Lukáš Adam & Martin Branda, 2016. "Nonlinear Chance Constrained Problems: Optimality Conditions, Regularization and Solvers," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 419-436, August.
    9. W. X. Zhu, 2003. "Penalty Parameter for Linearly Constrained 0–1 Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 116(1), pages 229-239, January.
    10. S. Lucidi & F. Rinaldi, 2010. "Exact Penalty Functions for Nonlinear Integer Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 145(3), pages 479-488, June.
    11. Singh, Vikas Vikram & Lisser, Abdel, 2019. "A second-order cone programming formulation for two player zero-sum games with chance constraints," European Journal of Operational Research, Elsevier, vol. 275(3), pages 839-845.
    12. Vikas Vikram Singh & Abdel Lisser, 2018. "A Characterization of Nash Equilibrium for the Games with Random Payoffs," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 998-1013, September.
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    Cited by:

    1. Abhishek Singh & Debdas Ghosh & Qamrul Hasan Ansari, 2024. "Inexact Newton Method for Solving Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 201(3), pages 1333-1363, June.

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