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Non-compact random generalized games and random quasi-variational inequalities. (English) Zbl 0821.47049

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.

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
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