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Single-Leader-Radner-Equilibrium: A New Approach for a Class of Bilevel Problems Under Uncertainty

Author

Listed:
  • Elisabetta Allevi

    (University of Brescia)

  • Didier Aussel

    (Université de Perpignan Via Domitia)

  • Rossana Riccardi

    (University of Brescia)

  • Domenico Scopelliti

    (University of Brescia)

Abstract

Bilevel problems with several followers, often called Single-Leader-Multi-Follower problems, have been proved to be very useful for modeling hierarchical interactions between agents in economics, industry, etc. When uncertainty must be taken into account, a classical approach is to use stochastic bilevel optimization. In this work, we introduce an alternative approach intrinsically integrating at the same time uncertain future and time-dependent decision processes. It is called Single-Leader-Radner-Equilibrium (SLRE) and is characterized by a hierarchical structure with one leader and several followers competing to reach a Radner equilibrium. A variational reformulation of the quasiconcave SLRE model (that is, where the objective function of the followers is only quasiconcave) is proposed and used to prove the existence of an optimistic solution of the quasiconcave SLRE. Finally, thanks to these developments we present a new approach of optimal design of eco-industrial parks.

Suggested Citation

  • Elisabetta Allevi & Didier Aussel & Rossana Riccardi & Domenico Scopelliti, 2024. "Single-Leader-Radner-Equilibrium: A New Approach for a Class of Bilevel Problems Under Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 344-370, January.
    • Handle: RePEc:spr:joptap:v:200:y:2024:i:1:d:10.1007_s10957-023-02339-5
    DOI: 10.1007/s10957-023-02339-5
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    References listed on IDEAS

    as
    1. Aussel, Didier & Cao Van, Kien & Salas, David, 2023. "Optimal design of exchange water networks with control inputs in Eco-Industrial Parks," Energy Economics, Elsevier, vol. 120(C).
    2. Johanna Burtscheidt & Matthias Claus, 2020. "Bilevel Linear Optimization Under Uncertainty," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 485-511, Springer.
    3. Limosani, Michele & Milasi, Monica & Scopelliti, Domenico, 2021. "Deregulated electricity market, a stochastic variational approach," Energy Economics, Elsevier, vol. 103(C).
    4. Monica Milasi & Domenico Scopelliti, 2021. "A Variational Approach to the Maximization of Preferences Without Numerical Representation," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 879-893, September.
    5. Didier Aussel & Anton Svensson, 2019. "Is Pessimistic Bilevel Programming a Special Case of a Mathematical Program with Complementarity Constraints?," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 504-520, May.
    6. D. Aussel & J. Cotrina, 2013. "Quasimonotone Quasivariational Inequalities: Existence Results and Applications," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 637-652, September.
    7. Maria Bernadette Donato & Monica Milasi & Antonio Villanacci, 2018. "Variational Formulation of a General Equilibrium Model with Incomplete Financial Markets and Numeraire Assets: Existence," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 425-451, November.
    8. Stephan Dempe, 2020. "Bilevel Optimization: Theory, Algorithms, Applications and a Bibliography," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 581-672, Springer.
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