Parameterized two-player nash equilibrium

Danny Hermelin; Chien Chung Huang; Stefan Kratsch; Magnus Wahlström

doi:10.1007/s00453-011-9609-z

Parameterized two-player nash equilibrium

Danny Hermelin, Chien Chung Huang, Stefan Kratsch, Magnus Wahlström

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

7 Scopus citations

Abstract

We study the problem of computing Nash equilibria in a two-player normal form (bimatrix) game from the perspective of parameterized complexity. Recent results proved hardness for a number of variants, when parameterized by the support size. We complement those results, by identifying three cases in which the problem becomes fixed-parameter tractable. Our results are based on a graph-theoretic representation of a bimatrix game, and on applying graph-theoretic tools on this representation.

Original language	English
Pages (from-to)	802-816
Number of pages	15
Journal	Algorithmica
Volume	65
Issue number	4
DOIs	https://doi.org/10.1007/s00453-011-9609-z
State	Published - 1 Apr 2013
Externally published	Yes

Keywords

Algorithms
Nash equilibrium
Parameterized complexity
Two-player games

ASJC Scopus subject areas

General Computer Science
Computer Science Applications
Applied Mathematics

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10.1007/s00453-011-9609-z

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title = "Parameterized two-player nash equilibrium",

abstract = "We study the problem of computing Nash equilibria in a two-player normal form (bimatrix) game from the perspective of parameterized complexity. Recent results proved hardness for a number of variants, when parameterized by the support size. We complement those results, by identifying three cases in which the problem becomes fixed-parameter tractable. Our results are based on a graph-theoretic representation of a bimatrix game, and on applying graph-theoretic tools on this representation.",

keywords = "Algorithms, Nash equilibrium, Parameterized complexity, Two-player games",

author = "Danny Hermelin and Huang, {Chien Chung} and Stefan Kratsch and Magnus Wahlstr{\"o}m",

note = "Funding Information: The third author acknowledges support by the Netherlands Organisation for Scientific Research (NWO), project “KERNELS: Combinatorial Analysis of Data Reduction”. ",

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doi = "10.1007/s00453-011-9609-z",

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T1 - Parameterized two-player nash equilibrium

AU - Hermelin, Danny

AU - Huang, Chien Chung

AU - Kratsch, Stefan

AU - Wahlström, Magnus

N1 - Funding Information: The third author acknowledges support by the Netherlands Organisation for Scientific Research (NWO), project “KERNELS: Combinatorial Analysis of Data Reduction”.

PY - 2013/4/1

Y1 - 2013/4/1

N2 - We study the problem of computing Nash equilibria in a two-player normal form (bimatrix) game from the perspective of parameterized complexity. Recent results proved hardness for a number of variants, when parameterized by the support size. We complement those results, by identifying three cases in which the problem becomes fixed-parameter tractable. Our results are based on a graph-theoretic representation of a bimatrix game, and on applying graph-theoretic tools on this representation.

AB - We study the problem of computing Nash equilibria in a two-player normal form (bimatrix) game from the perspective of parameterized complexity. Recent results proved hardness for a number of variants, when parameterized by the support size. We complement those results, by identifying three cases in which the problem becomes fixed-parameter tractable. Our results are based on a graph-theoretic representation of a bimatrix game, and on applying graph-theoretic tools on this representation.

KW - Algorithms

KW - Nash equilibrium

KW - Parameterized complexity

KW - Two-player games

UR - http://www.scopus.com/inward/record.url?scp=84893004445&partnerID=8YFLogxK

U2 - 10.1007/s00453-011-9609-z

DO - 10.1007/s00453-011-9609-z

M3 - Article

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VL - 65

SP - 802

EP - 816

JO - Algorithmica

JF - Algorithmica

IS - 4

ER -

Parameterized two-player nash equilibrium

Abstract

Keywords

ASJC Scopus subject areas

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