IJPAM: Volume 35, No. 3 (2007)

GENERIC STABILITY OF THE SET OF WEAKLY
PARETO-NASH EQUILIBRIUM POINTS

Xiaojun Yu$^1$, Zhi Lin$^2$
$^{1,2}$College of Mathematics and Statistics
Guizhou College of Finance and Economics
Guiyang, 550004, P.R. CHINA
$^1$e-mail: xjyu-myu@163.com
$^2$e-mail: linzhi7525@163.com


Abstract.In this paper, we study the existence of additive weight Nash-equilibrium and weakly Pareto-Nash equilibrium for multiobjective games. We prove that, for every multiobjective game has at least one additive weight weakly Pareto-Nash equilibrium with respect to the weight vector. As results, we show that in the sense of Baire categories, most multiobjective games have at least one essential weakly Pareto-Nash equilibrium points.

Received: December 1, 2006

AMS Subject Classification: 91A06, 91A10

Key Words and Phrases: multiobjective game, additive weight Nash equilibrium, weakly Pareto-Nash equilibrium, almost lower semicontinuous

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 35
Issue: 3