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On a Class of Multistage Stochastic Hierarchical Problems

Author

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  • Domenico Scopelliti

    (Department of Economics and Management, University of Brescia, Contrada S. Chiara 50, 25122 Brescia, Italy)

Abstract

In this paper, following the multistage stochastic approach proposed by Rockafellar and Wets, we analyze a class of multistage stochastic hierarchical problems: the Multistage Stochastic Optimization Problem with Quasi-Variational Inequality Constraints. Such a problem is defined in a suitable functional setting relative to a finite set of possible scenarios and certain information fields. The key of this multistage stochastic hierarchical problem turns out to be the nonanticipativity: some constraints have to be included in the formulation to take into account the partial information progressively revealed. In this way, we are able to study real-world problems in which the hierarchical decision processes are characterized by sequential decisions in response to an increasing level of information. As an application of this class of multistage stochastic hierarchical problems, we focus on the study of a suitable Single-Leader-Multi-Follower game.

Suggested Citation

  • Domenico Scopelliti, 2022. "On a Class of Multistage Stochastic Hierarchical Problems," Mathematics, MDPI, vol. 10(21), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4044-:d:958867
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    References listed on IDEAS

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    1. R. T. Rockafellar & Roger J.-B. Wets, 1991. "Scenarios and Policy Aggregation in Optimization Under Uncertainty," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 119-147, February.
    2. Maria Bernadette Donato & Antonino Maugeri & Monica Milasi & Antonio Villanacci, 2021. "Variational Inequalities and General Equilibrium Models," Springer Optimization and Its Applications, in: Ioannis N. Parasidis & Efthimios Providas & Themistocles M. Rassias (ed.), Mathematical Analysis in Interdisciplinary Research, pages 169-212, Springer.
    3. Limosani, Michele & Milasi, Monica & Scopelliti, Domenico, 2021. "Deregulated electricity market, a stochastic variational approach," Energy Economics, Elsevier, vol. 103(C).
    4. Shenglong Zhou & Alain B. Zemkoho & Andrey Tin, 2020. "BOLIB: Bilevel Optimization LIBrary of Test Problems," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 563-580, Springer.
    5. Arega Getaneh Abate & Rossana Riccardi & Carlos Ruiz, 2022. "Contract design in electricity markets with high penetration of renewables: A two-stage approach," Papers 2201.09927, arXiv.org, revised Jun 2022.
    6. Jong-Shi Pang & Masao Fukushima, 2005. "Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games," Computational Management Science, Springer, vol. 2(1), pages 21-56, January.
    7. Georgia Fargetta & Antonino Maugeri & Laura Scrimali, 2022. "A Stochastic Nash Equilibrium Problem for Medical Supply Competition," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 354-380, June.
    8. Abate, Arega Getaneh & Riccardi, Rossana & Ruiz, Carlos, 2022. "Contract design in electricity markets with high penetration of renewables: A two-stage approach," Omega, Elsevier, vol. 111(C).
    9. Didier Aussel & Anton Svensson, 2020. "A Short State of the Art on Multi-Leader-Follower Games," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 53-76, Springer.
    10. 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.
    11. Marco Castellani & Massimiliano Giuli & Massimo Pappalardo, 2018. "A Ky Fan Minimax Inequality for Quasiequilibria on Finite-Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 53-64, October.
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