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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.<\/jats:p>","DOI":"10.1007\/s10898-023-01282-z","type":"journal-article","created":{"date-parts":[[2023,4,3]],"date-time":"2023-04-03T10:23:20Z","timestamp":1680517400000},"page":"931-952","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the study of multistage stochastic vector quasi-variational problems"],"prefix":"10.1007","volume":"86","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9259-8916","authenticated-orcid":false,"given":"Elena","family":"Molho","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Domenico","family":"Scopelliti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,4,3]]},"reference":[{"key":"1282_CR1","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1023\/B:JOGO.0000035018.46514.ca","volume":"29","author":"QH Ansari","year":"2004","unstructured":"Ansari, Q.H., Chan, W.K., Yang, X.Q.: The system of vector quasi-equilibrium problems with applications. 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