Non-compact random generalized games and random quasi-variational inequalities. (1994)

• Record Type: Journal Article
• Authors: Yuan, Xian-Zhi
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 7:Number 4(1994)
• Page Start: 467
• Page End: 486
• Publication Date: 1994
• Subjects: Polish space -- Suslin space -- measurable space -- Suslin family -- (random) fixed point -- (random) maximal element -- (random) equilibria -- (random) qualitative game -- (random) generalized game -- (random) variational inequality -- (random) quasi-variational inequality -- class L -- L-majorized -- measurable selection theorem -- property (K) -- random operator; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953394000377
• Languages: English
• ISSNs: 1048-9533

Abstract

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.