On the existence of Pareto undominated mixed-strategy Nash equilibrium in normal-form games with infinite actions

Haifeng Fu

doi:10.1016/j.econlet.2021.109771

On the existence of Pareto undominated mixed-strategy Nash equilibrium in normal-form games with infinite actions

Haifeng Fu^*

^*Corresponding author for this work

Department of Economics

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

7 Citations (Scopus)

Abstract

We show that each mixed strategy of a normal-form game can be reformulated as a pure strategy of an induced Bayesian game. Moreover, a normal-form game has a Pareto undominated mixed-strategy Nash equilibrium if and only if its induced Bayesian game has a pure-strategy Bayesian Nash equilibrium. By relying on the existence result of Pareto undominated pure-strategy Nash equilibrium in Bayesian games in Fu and Yu (2015), we also show that every normal-form game has a Pareto undominated mixed-strategy Nash equilibrium.

Original language	English
Article number	109771
Journal	Economics Letters
Volume	201
DOIs	https://doi.org/10.1016/j.econlet.2021.109771
Publication status	Published - Apr 2021

Keywords

Bayesian game
Normal-form game
Pareto undominated mixed-strategy Nash equilibrium
Pareto undominated pure-strategy Bayesian Nash equilibrium

Access to Document

10.1016/j.econlet.2021.109771

Cite this

Fu, H. (2021). On the existence of Pareto undominated mixed-strategy Nash equilibrium in normal-form games with infinite actions. Economics Letters, 201, Article 109771. https://doi.org/10.1016/j.econlet.2021.109771

@article{dc430c26f2bb4eaf8d03345cc2c0604c,

title = "On the existence of Pareto undominated mixed-strategy Nash equilibrium in normal-form games with infinite actions",

abstract = "We show that each mixed strategy of a normal-form game can be reformulated as a pure strategy of an induced Bayesian game. Moreover, a normal-form game has a Pareto undominated mixed-strategy Nash equilibrium if and only if its induced Bayesian game has a pure-strategy Bayesian Nash equilibrium. By relying on the existence result of Pareto undominated pure-strategy Nash equilibrium in Bayesian games in Fu and Yu (2015), we also show that every normal-form game has a Pareto undominated mixed-strategy Nash equilibrium.",

keywords = "Bayesian game, Normal-form game, Pareto undominated mixed-strategy Nash equilibrium, Pareto undominated pure-strategy Bayesian Nash equilibrium",

author = "Haifeng Fu",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

year = "2021",

month = apr,

doi = "10.1016/j.econlet.2021.109771",

language = "English",

volume = "201",

journal = "Economics Letters",

issn = "0165-1765",

}

TY - JOUR

T1 - On the existence of Pareto undominated mixed-strategy Nash equilibrium in normal-form games with infinite actions

AU - Fu, Haifeng

PY - 2021/4

Y1 - 2021/4

N2 - We show that each mixed strategy of a normal-form game can be reformulated as a pure strategy of an induced Bayesian game. Moreover, a normal-form game has a Pareto undominated mixed-strategy Nash equilibrium if and only if its induced Bayesian game has a pure-strategy Bayesian Nash equilibrium. By relying on the existence result of Pareto undominated pure-strategy Nash equilibrium in Bayesian games in Fu and Yu (2015), we also show that every normal-form game has a Pareto undominated mixed-strategy Nash equilibrium.

AB - We show that each mixed strategy of a normal-form game can be reformulated as a pure strategy of an induced Bayesian game. Moreover, a normal-form game has a Pareto undominated mixed-strategy Nash equilibrium if and only if its induced Bayesian game has a pure-strategy Bayesian Nash equilibrium. By relying on the existence result of Pareto undominated pure-strategy Nash equilibrium in Bayesian games in Fu and Yu (2015), we also show that every normal-form game has a Pareto undominated mixed-strategy Nash equilibrium.

KW - Bayesian game

KW - Normal-form game

KW - Pareto undominated mixed-strategy Nash equilibrium

KW - Pareto undominated pure-strategy Bayesian Nash equilibrium

UR - http://www.scopus.com/inward/record.url?scp=85100888136&partnerID=8YFLogxK

U2 - 10.1016/j.econlet.2021.109771

DO - 10.1016/j.econlet.2021.109771

M3 - Article

AN - SCOPUS:85100888136

SN - 0165-1765

VL - 201

JO - Economics Letters

JF - Economics Letters

M1 - 109771

ER -

On the existence of Pareto undominated mixed-strategy Nash equilibrium in normal-form games with infinite actions

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this