On a Class of Multistage Stochastic Hierarchical Problems

Domenico Scopelliti
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Domenico Scopelliti: Department of Economics and Management, University of Brescia, Contrada S. Chiara 50, 25122 Brescia, Italy

Mathematics, 2022, vol. 10, issue 21, 1-13

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.

Keywords: hierarchical problem; Optimization Problem with Quasi-Variational Inequality Constraints; multistage stochastic variational inequality; Single-Leader-Multi-Follower game (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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