Journal of Applied Mathematics and Stochastic Analysis
Volume 7 (1994), Issue 4, Pages 467-486
Non-compact random generalized games and random quasi-variational inequalities
1Department of Mathematics, Statistics, and Computing Science, Dalhousie University, N.S., Halifax B3H 3J5, Canada
2Department of Mathematics, The University of Queensland, Brisbane 4072, Australia
Received 1 October 1993; Revised 1 June 1994
Copyright © 1994 Xian-Zhi Yuan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper, existence theorems of random maximal elements, random
equilibria for the random one-person game and random generalized game with a
countable number of players are given as applications of random fixed point
theorems. By employing existence theorems of random generalized games, we
deduce the existence of solutions for non-compact random quasi-variational inequalities. These in turn are used to establish several existence theorems of noncompact generalized random quasi-variational inequalities which are either
stochastic versions of known deterministic inequalities or refinements of corresponding results known in the literature.