A reaction-diffusion system arising in game theory: Existence of solutions and spatial dominance

Hideo Deguchi

doi:10.3934/dcdsb.2017200

A reaction-diffusion system arising in game theory: Existence of solutions and spatial dominance

Hideo Deguchi^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The initial value problem for a reaction-diffusion system with discontinuous nonlinearities proposed by Hofbauer in 1999 as an equilibrium selection model in game theory is studied from the viewpoint of the existence and stability of solutions. An equilibrium selection result using the stability of a constant stationary solution is obtained for finite symmetric 2 person games with a 1/2-dominant equilibrium.

Original language	English
Pages (from-to)	3891-3901
Number of pages	11
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	22
Issue number	10
DOIs	https://doi.org/10.3934/dcdsb.2017200
State	Published - 2017/12

Keywords

Discontinuous nonlinearities
Equilibrium selection
Existence
Game theory
Initial value problem
Reaction-diffusion system
Stability

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcdsb.2017200

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title = "A reaction-diffusion system arising in game theory: Existence of solutions and spatial dominance",

abstract = "The initial value problem for a reaction-diffusion system with discontinuous nonlinearities proposed by Hofbauer in 1999 as an equilibrium selection model in game theory is studied from the viewpoint of the existence and stability of solutions. An equilibrium selection result using the stability of a constant stationary solution is obtained for finite symmetric 2 person games with a 1/2-dominant equilibrium.",

keywords = "Discontinuous nonlinearities, Equilibrium selection, Existence, Game theory, Initial value problem, Reaction-diffusion system, Stability",

author = "Hideo Deguchi",

note = "Funding Information: Acknowledgments. This work was supported in part by Grant for Basic Science Research Projects from The Sumitomo Fundation (No. 110244) and JSPS KAK-ENHI Grant Number JP24740083. Part of this work was done while the author Figure 3. {\textcopyright}i is the set of u ∈ ∆ to which the pure strategy i (i.e., ei) is the best reply in the game (14) for i = 1, 2, 3. The three dots denote the middle points of the edges.",

year = "2017",

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doi = "10.3934/dcdsb.2017200",

language = "英語",

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N2 - The initial value problem for a reaction-diffusion system with discontinuous nonlinearities proposed by Hofbauer in 1999 as an equilibrium selection model in game theory is studied from the viewpoint of the existence and stability of solutions. An equilibrium selection result using the stability of a constant stationary solution is obtained for finite symmetric 2 person games with a 1/2-dominant equilibrium.

AB - The initial value problem for a reaction-diffusion system with discontinuous nonlinearities proposed by Hofbauer in 1999 as an equilibrium selection model in game theory is studied from the viewpoint of the existence and stability of solutions. An equilibrium selection result using the stability of a constant stationary solution is obtained for finite symmetric 2 person games with a 1/2-dominant equilibrium.

KW - Discontinuous nonlinearities

KW - Equilibrium selection

KW - Existence

KW - Game theory

KW - Initial value problem

KW - Reaction-diffusion system

KW - Stability

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SN - 1531-3492

VL - 22

SP - 3891

EP - 3901

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 10

ER -

A reaction-diffusion system arising in game theory: Existence of solutions and spatial dominance

Abstract

Keywords

ASJC Scopus subject areas

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