  This paper focuses on the solvability of multistage pseudomonotone stochastic
variational inequalities (SVIs). On one hand, some known solvability results of
pseudomonotone deterministic variational inequalities cannot be directly
extended to pseudomonotone SVIs, so we construct the isomorphism between both
and then establish theoretical results on the existence, convexity, boundedness
and compactness of the solution set for pseudomonotone SVIs via such an
isomorphism. On the other hand, the progressive hedging algorithm (PHA) is an
important and effective method for solving monotone SVIs, but it cannot be
directly used to solve nonmonotone SVIs. We propose some sufficient conditions
on the elicitability of pseudomonotone SVIs, which opens the door for applying
elicited PHA to solve pseudomonotone SVIs. Numerical results on solving a
pseudomonotone two-stage stochastic market optimization problem and randomly
generated two stage pseudomonotone linear complementarity problems are
presented to show the efficiency of the elicited PHA for solving pseudomonotone
SVIs.
