A comparison of discrete fixed point theorems via a bimatrix game

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

There are three types of discrete fixed point theorems: type M and type C deal with monotone mappings and contraction mappings, respectively. Type B is based on Brouwer's fixed point theorem. The main aim of this paper is to compare type B with type M by applying them to a bimatrix game. For this purpose we characterize the direction preserving condition that is used in type B in terms of the best response mappings of the bimatrix game. Further we extend the characterization to a non-cooperative n-person game.

Original languageEnglish
Pages (from-to)1501-1510
Number of pages10
JournalJournal of Nonlinear and Convex Analysis
Volume16
Issue number8
Publication statusPublished - 2015

Fingerprint

Bimatrix Games
Fixed point theorem
Brouwer Fixed Point Theorem
Monotone Mapping
Contraction Mapping
Person
Game

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology
  • Control and Optimization
  • Applied Mathematics

Cite this

A comparison of discrete fixed point theorems via a bimatrix game. / Kawasaki, Hidefumi.

In: Journal of Nonlinear and Convex Analysis, Vol. 16, No. 8, 2015, p. 1501-1510.

Research output: Contribution to journalArticle

@article{a208b456a62d4067a3aef5220bd3822c,
title = "A comparison of discrete fixed point theorems via a bimatrix game",
abstract = "There are three types of discrete fixed point theorems: type M and type C deal with monotone mappings and contraction mappings, respectively. Type B is based on Brouwer's fixed point theorem. The main aim of this paper is to compare type B with type M by applying them to a bimatrix game. For this purpose we characterize the direction preserving condition that is used in type B in terms of the best response mappings of the bimatrix game. Further we extend the characterization to a non-cooperative n-person game.",
author = "Hidefumi Kawasaki",
year = "2015",
language = "English",
volume = "16",
pages = "1501--1510",
journal = "Journal of Nonlinear and Convex Analysis",
issn = "1345-4773",
publisher = "Yokohama Publishers",
number = "8",

}

TY - JOUR

T1 - A comparison of discrete fixed point theorems via a bimatrix game

AU - Kawasaki, Hidefumi

PY - 2015

Y1 - 2015

N2 - There are three types of discrete fixed point theorems: type M and type C deal with monotone mappings and contraction mappings, respectively. Type B is based on Brouwer's fixed point theorem. The main aim of this paper is to compare type B with type M by applying them to a bimatrix game. For this purpose we characterize the direction preserving condition that is used in type B in terms of the best response mappings of the bimatrix game. Further we extend the characterization to a non-cooperative n-person game.

AB - There are three types of discrete fixed point theorems: type M and type C deal with monotone mappings and contraction mappings, respectively. Type B is based on Brouwer's fixed point theorem. The main aim of this paper is to compare type B with type M by applying them to a bimatrix game. For this purpose we characterize the direction preserving condition that is used in type B in terms of the best response mappings of the bimatrix game. Further we extend the characterization to a non-cooperative n-person game.

UR - http://www.scopus.com/inward/record.url?scp=84940908520&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84940908520&partnerID=8YFLogxK

M3 - Article

VL - 16

SP - 1501

EP - 1510

JO - Journal of Nonlinear and Convex Analysis

JF - Journal of Nonlinear and Convex Analysis

SN - 1345-4773

IS - 8

ER -