A Note on Gale, Kuhn, and Tucker’s Reductions of Zero-Sum Games☆

Shuige Liu

A Note on Gale, Kuhn, and Tucker’s Reductions of Zero-Sum Games☆

School of Political Science and Economics

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

Abstract

Gale, Kuhn and Tucker [1] introduced two ways to reduce a zero-sum game by packaging some strategies with respect to a probability distribution on them. In terms of value, they gave conditions for a desirable reduction. We show that a probability distribution for a desirable reduction relies on optimal strategies in the original game. Also, we correct an improper example given by them to show that the reverse of a theorem does not hold.

Original language	English
Journal	Unknown Journal
Publication status	Published - 2017 Oct 6

Keywords

Maximin value
Optimal strategy
Reduction
Zero-sum game

ASJC Scopus subject areas

General

Fingerprint Dive into the research topics of 'A Note on Gale, Kuhn, and Tucker’s Reductions of Zero-Sum Games☆'. Together they form a unique fingerprint.

Cite this

@article{806077ed8eed4947bf70bc9511b4ab05,

title = "A Note on Gale, Kuhn, and Tucker{\textquoteright}s Reductions of Zero-Sum Games☆",

abstract = "Gale, Kuhn and Tucker [1] introduced two ways to reduce a zero-sum game by packaging some strategies with respect to a probability distribution on them. In terms of value, they gave conditions for a desirable reduction. We show that a probability distribution for a desirable reduction relies on optimal strategies in the original game. Also, we correct an improper example given by them to show that the reverse of a theorem does not hold.",

keywords = "Maximin value, Optimal strategy, Reduction, Zero-sum game",

author = "Shuige Liu",

year = "2017",

month = oct,

day = "6",

language = "English",

journal = "Nuclear Physics A",

issn = "0375-9474",

publisher = "Elsevier",

}

TY - JOUR

T1 - A Note on Gale, Kuhn, and Tucker’s Reductions of Zero-Sum Games☆

AU - Liu, Shuige

PY - 2017/10/6

Y1 - 2017/10/6

N2 - Gale, Kuhn and Tucker [1] introduced two ways to reduce a zero-sum game by packaging some strategies with respect to a probability distribution on them. In terms of value, they gave conditions for a desirable reduction. We show that a probability distribution for a desirable reduction relies on optimal strategies in the original game. Also, we correct an improper example given by them to show that the reverse of a theorem does not hold.

AB - Gale, Kuhn and Tucker [1] introduced two ways to reduce a zero-sum game by packaging some strategies with respect to a probability distribution on them. In terms of value, they gave conditions for a desirable reduction. We show that a probability distribution for a desirable reduction relies on optimal strategies in the original game. Also, we correct an improper example given by them to show that the reverse of a theorem does not hold.

KW - Maximin value

KW - Optimal strategy

KW - Reduction

KW - Zero-sum game

UR - http://www.scopus.com/inward/record.url?scp=85093002022&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85093002022&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85093002022

JO - Nuclear Physics A

JF - Nuclear Physics A

SN - 0375-9474

ER -