International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 1, Pages 179-189

Maximal elements and equilibria of generalized games for 𝒰-majorized and condensing correspondences

George Xian-Zhi Yuan1,2 and E. Tarafdar2

1Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia B3H 3J5, Canada
2Department of Mathematics, The University of Queensland, Brisbane 4072, Australia

Received 29 November 1993; Revised 10 October 1996

Copyright © 1999 George Xian-Zhi Yuan and E. Tarafdar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, we first give an existence theorem of maximal elements for a new type of preference correspondences which are 𝒰-majorized. Then some existence theorems for compact (resp., non-compact) qualitative games and generalized games in which the constraint or preference correspondences are 𝒰-majorized (resp., Ψ-condensing) are obtained in locally convex topological vector spaces.