On the study of multistage stochastic vector quasi-variational problems

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