On Essential Components of the Solution Set of Generalized Games

Abstract

In this paper, we prove that for any generalized game, there exists at least one essential connected component of the set of it's equilibrium points. ᮊ 1999 Academic Press 303 0022-247Xr99 $30.00

Stability of fixed points of set-valued mappings and strategic stability of Nash equilibria

“…Yu and Xiang [26] proposed an essential set for Nash equilibria and proved the existence of essential component in the second direction by considering perturbations of payoff functions of players. There is a lot of researches about using the essential component to discuss the stability of Nash equilibria (see, [1,2,8,17,18,24,25,27]). However, there are two drawbacks in the second way.…”

Berge's maximum theorem to vector-valued functions with some applications

“…Obviously, our results are established for vector-valued payoff function with weaker continuity and stronger convexity, so the results cannot include many present results in the literatures. What is more, Theorem 5.5 and Theorem 5.7 on the essential components of the equilibrium sets are derived in the uniform topology of best-reply correspondences, which are different from the existence results in [12,13,26,29,30] in the uniform topology of payoff functions and feasible strategy correspondences. The following two examples will show that the two kinds of topology are not equivalent.…”

“…(see [4,21,22,25,27]). Motivated by [11][12][13][14], we shall give some existence of essential components of the set of weakly Pareto-Nash equilibrium for such games, which have been studied in [26,29,30]. Some examples are given to investigate our results.…”

The essential components of the set of equilibrium points for set-valued maps

“…In recent years, much attention has been devoted to essential components of the solution set for nonlinear problems such as Ky Fan's point problems, coincidence point problems and Nash equilibrium point problems, etc. see [5,6,[9][10][11][12].…”