A Further Generalization of the Kakutani Fixed Point Theorem, with Application to Nash Equilibrium Points

1952 ◽  
Vol 3 (1) ◽  
pp. 170 ◽  
Author(s):  
I. L. Glicksberg
Keyword(s):  
Fixed Point ◽  
Nash Equilibrium ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Equilibrium Points ◽  
Nash Equilibrium Points ◽  
Kakutani Fixed Point ◽  
Kakutani Fixed Point Theorem

A fuzzy fixed-point theorem and its applications to maximal elements and Nash equilibria in noncompact CAT(0) spaces

2022 ◽  
pp. 1-18
Author(s):  
Haishu Lu ◽  
Rong Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Maximal Element ◽  
Existence Theorems ◽  
Equilibrium Points ◽  
Maximal Elements ◽  
Nash Equilibrium Points ◽  
Fuzzy Fixed Point ◽  
Qualitative Games

In this paper, based on the KKM method, we prove a new fuzzy fixed-point theorem in noncompact CAT(0) spaces. As applications of this fixed-point theorem, we obtain some existence theorems of fuzzy maximal element points. Finally, we utilize these fuzzy maximal element theorems to establish some new existence theorems of Nash equilibrium points for generalized fuzzy noncooperative games and fuzzy noncooperative qualitative games in noncompact CAT(0) spaces. The results obtained in this paper generalize and extend many known results in the existing literature.

scholarly journals Existence of a Short-Run Equilibrium of the Dixit-Stiglitz-Krugman Model

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Minoru Tabata ◽  
Nobuoki Eshima
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Nonlinear Operator ◽  
Wage Equation ◽  
Short Run ◽  
Kakutani Fixed Point ◽  
Kakutani Fixed Point Theorem

Each short-run equilibrium of the Dixit-Stiglitz-Krugman model is defined as a solution to the wage equation when the distributions of workers and farmers are given functions. We extend the discrete nonlinear operator contained in the wage equation as a set-valued operator. Applying the Kakutani fixed-point theorem to the set-valued operator, under the most general assumptions, we prove that the model has a short-run equilibrium.

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