scholarly journals Pure strategy Nash equilibrium points and the Lefschetz fixed point theorem

1983 ◽  
Vol 12 (3) ◽  
pp. 181-191 ◽  
Author(s):  
L. Tesfatsion
Keyword(s):  
Fixed Point ◽  
Nash Equilibrium ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Equilibrium Points ◽  
Pure Strategy ◽  
Nash Equilibrium Points ◽  
Lefschetz Fixed Point Theorem ◽  
Strategy Nash Equilibrium

AN APPLICATION OF A DISCRETE FIXED POINT THEOREM TO A GAME IN EXPANSIVE FORM

2013 ◽  
Vol 30 (03) ◽  
pp. 1340013 ◽  
Author(s):  
HIDEFUMI KAWASAKI ◽  
AKIFUMI KIRA ◽  
SHINPEI KIRA
Keyword(s):  
Fixed Point ◽  
Nash Equilibrium ◽  
Fixed Point Theorem ◽  
Existence Theorem ◽  
Point Theorem ◽  
Pure Strategy ◽  
Contraction Mappings ◽  
Person Game ◽  
Strategy Nash Equilibrium

In this paper, we first present a discrete fixed point theorem for contraction mappings from the product set of integer intervals into itself, which is an extension of Robert's discrete fixed point theorem. Next, we derive an existence theorem of a pure-strategy Nash equilibrium for a noncooperative n-person game from our fixed point theorem. Finally, we show that Kuhn's theorem for a game in expansive form can be explained by our existence 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 Lefschetz fixed point theorem for acyclic maps with multiplicity

2002 ◽  
Vol 19 (2) ◽  
pp. 339 ◽  
Author(s):  
Fritz Von Haeseler ◽  
Heinz-Otto Peitgen ◽  
Gencho Skordev
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Lefschetz Fixed Point Theorem

Finding the Pure-Strategy Nash Equilibrium Using a Fixed-Point Algorithm

2013 ◽  
Vol 427-429 ◽  
pp. 1803-1806 ◽  
Author(s):  
Zheng Tian Wu ◽  
Chuang Yin Dang ◽  
Chang An Zhu
Keyword(s):  
Fixed Point ◽  
Nash Equilibrium ◽  
Normal Form ◽  
Pure Strategy ◽  
Payoff Function ◽  
Fixed Point Algorithm ◽  
Linear Programming Formulation ◽  
Active Research ◽  
Person Game ◽  
Strategy Nash Equilibrium

It is well known that determining whether a finite game has a pure-strategy Nash equilibrium is an NP-hard problem and it is an active research topic to find a Nash equilibrium recently. In this paper, an implementation of Dang's Fixed-Point iterative method is introduced to find a pure-strategy Nash equilibrium of a finite n-person game in normal form. There are two steps to find one pure-strategy Nash equilibrium in this paper. The first step is converting the problem to a mixed 0-1 linear programming formulation based on the properties of pure strategy and multilinear terms in the payoff function. In the next step, the Dangs method is used to solve the formulation generated in the former step. Numerical results show that this method is effective to find a pure-strategy Nash equilibrium of a finite n-person game in normal form.

ON SOME NONAUTONOMOUS CHAOTIC SYSTEM ON THE PLANE

1999 ◽  
Vol 09 (09) ◽  
pp. 1853-1858 ◽  
Author(s):  
KLAUDIUSZ WÓJCIK
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Fixed Point Theorem ◽  
Chaotic System ◽  
Point Theorem ◽  
Chaotic Behavior ◽  
Topological Methods ◽  
Lefschetz Fixed Point Theorem ◽  
Nonautonomous Equations ◽  
Time Periodic

We prove the existence of the chaotic behavior in dynamical systems generated by some class of time periodic nonautonomous equations on the plane. We use topological methods based on the Lefschetz Fixed Point Theorem and the Ważewski Retract Theorem.

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