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Nonlinear Analysis 54 (2003) 525543 www.elsevier.com/locate/na

Summary: Nonlinear Analysis 54 (2003) 525­543
On the constrained equilibrium problems with
˙nite families of players
Lai-Jiu Lina;, Shih Feng Chenga, Xu Yao Liua, Q.H. Ansarib
aDepartment of Mathematics, National Changhua University of Education,
Changhua, Taiwan 50058, People's Republic of China
bDepartment of Mathematics, Aligarh Muslim University, Aligarh 202 002, India
Received 30 January 2002; accepted 22 November 2002
In this paper, we consider the equilibrium problem with ˙nite number of families of players
such that each family may not have the same number of players and ˙nite number of families
of constrained correspondences on the strategy sets. We also consider the case with two ˙nite
families of constrained correspondences on the strategies sets. We demonstrate an example of
our equilibrium problem. We derive a ˙xed point theorem for a family of multimaps and a
coincidence theorem for two families of multimaps. By using these results, we establish the
existence of a solution of our equilibrium problems. The results of this paper generalize some
known results in the literature.
? 2003 Elsevier Science Ltd. All rights reserved.
Keywords: Constrained equilibrium problems; Debreu Social equilibrium problem; Nash equilibrium problem;


Source: Ansari, Qamrul Hasan - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals


Collections: Mathematics