Yuan, Xian-Zhi Non-compact random generalized games and random quasi-variational inequalities. (English) Zbl 0821.47049 J. Appl. Math. Stochastic Anal. 7, No. 4, 467-486 (1994). Summary: 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 non- compact generalized random quasi-variational inequalities which are either stochastic versions of known deterministic inequalities or refinements of corresponding results known in the literature. Cited in 7 Documents MSC: 47H40 Random nonlinear operators 47H10 Fixed-point theorems 47B80 Random linear operators 47H04 Set-valued operators 47J20 Variational and other types of inequalities involving nonlinear operators (general) 47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics 49J40 Variational inequalities 49J45 Methods involving semicontinuity and convergence; relaxation 49J55 Existence of optimal solutions to problems involving randomness 54C60 Set-valued maps in general topology 60H25 Random operators and equations (aspects of stochastic analysis) 91B50 General equilibrium theory 91A07 Games with infinitely many players 91A60 Probabilistic games; gambling 28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence Keywords:random maximal elements; existence theorems; random equilibria; random one-person game; random generalized game with a countable number of players; random fixed point theorems; non-compact random quasi- variational inequalities PDFBibTeX XMLCite \textit{X.-Z. Yuan}, J. Appl. Math. Stochastic Anal. 7, No. 4, 467--486 (1994; Zbl 0821.47049) Full Text: DOI EuDML