Existence of equilibrium in generalized games with non-convex strategy spaces
We analyze the existence of equilibrium in generalized games in a framework without any linear structure (where the usual convexity notion can not be defined) by using an abstract convexity structure called mc-spaces. In particular we replace the convexity condition on the strategy spaces and the images of preference and constraint correspondences by the notion of mc-set (which generalizes the notion of convex set). Among others, our results generalize those of Borglin and Keiding, Shafer and Sonnenschein, Border and Tulcea.
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