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.

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.

scholarly journals (α,ψ)-Meir-Keeler Contraction Mappings in Generalized b-Metric Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-4 ◽  
Author(s):  
Erdal Karapinar ◽  
Stefan Czerwik ◽  
Hassen Aydi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contraction Mappings

We present a fixed point theorem for generalized (α,ψ)-Meir-Keeler type contractions in the setting of generalized b-metric spaces. The presented results improve, generalize, and unify many existing famous results in the corresponding literature.

scholarly journals A General Fixed Point Theorem For Implicit Cyclic Multi-Valued Contraction Mappings

2015 ◽  
Vol 29 (1) ◽  
pp. 119-129 ◽  
Author(s):  
Valeriu Popa
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Implicit Relation ◽  
Contraction Mappings

AbstractIn this paper, a general fixed point theorem for cyclic multi-valued mappings satisfying an implicit relation from [19] different from implicit relations used in [13] and [23], generalizing some results from [22], [15], [13], [14], [16], [10] and from other papers, is proved.

scholarly journals Suzuki-Type Generalization of Chatterjea Contraction Mappings on Complete Partial Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Mohammad Imdad ◽  
Ali Erduran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Partial Metric ◽  
Contraction Mappings ◽  
Partial Metric Spaces

Motivated by Suzuki (2008), we prove a Suzuki-type fixed point theorem employing Chatterjea contraction on partial metric spaces.

scholarly journals Some variants of Wardowski fixed point theorem

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Muhammad Nazam ◽  
Hassen Aydi ◽  
Choonkil Park ◽  
Muhammad Arshad ◽  
Ekrem Savas ◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Contraction Mappings

AbstractThe purpose of this paper is to consider some F-contraction mappings in a dualistic partial metric space and to provide sufficient related conditions for the existence of a fixed point. The obtained results are extensions of several ones existing in the literature. Moreover, we present examples and an application to support our results.

A Fixed Point Theorem for Semigroups of Proximately Uniformly Lipschitzian Mappings

1991 ◽  
Vol 34 (4) ◽  
pp. 559-562
Author(s):  
Hong-Kun Xu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Existence Theorem ◽  
Point Theorem ◽  
Common Fixed Points ◽  
Nonexpansive Semigroups ◽  
Lipschitzian Mappings ◽  
Lipschitzian Semigroup

AbstractAs a generalization of Kiang and Tan's proximately nonexpansive semigroups, the notion of a proximately uniformly Lipschitzian semigroup is introduced and an existence theorem of common fixed points for such a semigroup is proved in a Banach space whose characteristic of convexity is less than one.

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