On the study of multistage stochastic vector quasi-variational problems

Elena Molho () and Domenico Scopelliti ()
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Elena Molho: University of Pavia
Domenico Scopelliti: Department of Economics and Management

Journal of Global Optimization, 2023, vol. 86, issue 4, No 6, 952 pages

Abstract: Abstract This paper focuses on the study of multistage stochastic vector generalized quasi-variational inequalities with a variable ordering structure. The proposed multistage stochastic vector quasi-variational problems are defined in a suitable functional setting relative to a finite set of final possible states and certain information fields; these formulations are a multicriteria extension of the multistage stochastic variational inequalities. A relevant aspect of these problems is the presence of the nonanticipativity constraints on the variables of the problem; stage by stage, these constraints impose the measurability with respect to the information field at that stage. Without requiring any assumption of monotonicity, we prove some existence results by using a nonlinear scalarization technique. On this basis, we analyze multistage stochastic vector Nash equilibrium problems: as an example, we focus on a suitable multistage stochastic bicriteria Cournot oligopolistic model.

Keywords: Multistage stochastic vector variational inequality; Nonlinear scalarization function; Nonanticipativity; Variable ordering structure; Generalized Nash-Cournot game (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-023-01282-z

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