On constrained generalized games with action sets in non-locally-convex and non-Hausdorff topological vector spaces

Abstract

This paper presents results on the existence of an equilibrium in the context of a typology consisting of qualitative, generalized and constrained generalized normal form games with the following features: (i) a set of players of arbitrary cardinality, (ii) action sets that may be non-compact subsets of a non-Hausdorff and non-locally convex space, (iii) individual preferences satisfying a weakened continuity postulate with origins in the literature on discontinuous strategic-form games. It reports four theorems and seven corollaries, and thereby brings together lines of work in game theory, Walrasian general equilibrium theory and applied mathematics in a synthetic overview that revolves around Browder’s fixed point theorem.