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The study of equilibria for abstract economics in topological vector spaces – a unified approach. (English) Zbl 0943.47053
This article presents the author’s attempt to “give a unified approach to study the existence of maximal elements and equilibria for qualitative games, generalized games in topological vector spaces and locally convex topological vector spaces”. The author formulates a new variant of the existence theorem for maximal elements, which covers a long list of results of previous investigators, and, furthermore, as applications of this new theorem, he proves equilibrium existence theorems for a non-compact one-person game and non-compact qualitative game with an infinite number of players and some special correspondences. The last part deals with the concept “approximate equilibria” and the existence theorems for the games when constraint mappings are lower semicontinuous instead of having open inverse values. The author states that his results unify and improve results from more than forty articles written since 1954 till 1995 by C. Aliprants and D. Brown, K. J. Arrow and G. Debreu, J. P. Aubin, H. Ben-El-Mechaiekh and P. Deguire, F. E. Browder, K. Fan, D. Gale and A. Mas-Collel, M. A. Khan and R. Papageorgiou, C. I. Tulcea, and others.
MSC:
47J30Variational methods (nonlinear operator equations)
91B50General equilibrium theory in economics
47H04Set-valued operators