Abstract
This paper provides sufficient conditions for the existence of solutions for quasiequilibrium problems and generalized game problems in the setting of infinite-dimensional metrizable spaces. To this purpose, we prove a modified version of a selection theorem due to Michael [15] by exploiting the fact that any compact set in a metric space is both complete and separable. Thereafter, by a fixed point technique which is based on the notion of inside point of a convex set, we provide some existence results without requiring the upper semicontinuity and the closed-valuedness of the feasibility maps.
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