Journal of Applied Mathematics and Stochastic Analysis 
Volume 7 (1994), Issue 4, Pages 467-486
doi:10.1155/S1048953394000377

Non-compact random generalized games and random quasi-variational inequalities

Xian-Zhi Yuan1,2

 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

Abstract

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.