International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 791-800

Equilibrium points of random generalized games

E. Tarafdar1 and Xian-Zhi Yuan1,2

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

Received 13 July 1993; Revised 30 August 1995

Copyright © 1998 E. Tarafdar and Xian-Zhi Yuan. 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, the concepts of random maximal elements, random equilibria and random generalized games are described. Secondly by measurable selection theorem, some existence theorems of random maximal elements for Lc-majorized correspondences are obtained. Then we prove existence theorems of random equilibria for non-compact one-person random games. Finally, a random equilibrium existence theorem for non-compact random generalized games (resp., random abstract economics) in topological vector spaces and a random equilibrium existence theorem of non-compact random games in locally convex topological vector spaces in which the constraint mappings are lower semicontinuous with countable number of players (resp., agents) are given. Our results are stochastic versions of corresponding results in the recent literatures.