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In this note, we investigate stochastic Nash equilibrium problems by means of monotone variational inequalities in probabilistic Lebesgue spaces. We apply our approach to a class of oligopolistic market equilibrium problems, where the data are known through their probability distributions. [ABSTRACT FROM AUTHOR]

We consider a class of parametric variational inequalities where both the operator and the convex set depend on time. This kind of variational inequalities are useful to model many time dependent equilibrium problems. We study the Lipschitz continuity of the solutions with respect to the time parameter and construct approximations for them which minimize the average worst case error. Some improved estimates of the Lipschitz constant for this class of problems are given. In order to illustrate our procedure, we study a classical network equilibrium problem. [ABSTRACT FROM AUTHOR]

We consider a class of parametric variational inequalities which, under suitable assumptions, admit an equivalent integral formulation. We study the Lipschitz continuity of the solution and treat in detail the case in which the parametric constraint set is a polytope. Finally, the results obtained are applied to the time-dependent traffic equilibrium problem. [ABSTRACT FROM AUTHOR]

We provide an equivalent formulation of a previously proposed noniterative algorithm (see A. Maugeri, Appl. Math. Optim. 16, 169-185, 1987) for the traffic equilibrium problem. Moreover, under the strict monotonicity assumption, we provide an improved algorithm which enlarges the range of applicability of the previous algorithm and decreases considerably its computational effort. Our algorithm is based on a general algorithm for variational inequalities (see O. Mancino, G. Stampacchia, J. Optim. Theory Appl. 9, 3-23, 1972), which we further develop and adapt to the traffic equilibrium problem. Both our proofs and the algorithm exploit directly the equilibrium conditions which characterize our problem. [ABSTRACT FROM AUTHOR]

We show that the problem of solving a certain class of time dependent variational inequalities is equivalent to the one of finding the stationary solutions of a related class of constrained dynamical systems. We exploit this equivalence to analyse the time dependent complementary problem. [Copyright &y& Elsevier]