research-article

Application of Nash Equilibrium in Two-Person Games

Authors:

Jun WenAuthors Info & Claims

ICIBE '21: Proceedings of the 7th International Conference on Industrial and Business Engineering

Pages 164 - 167

https://doi.org/10.1145/3494583.3494645

Published: 09 January 2022 Publication History

Get Access

Abstract

Game theory is the study of the ways in which interacting choices of economic agents produce outcomes with respect to the preferences of those agents. The outcomes in question might have been intended by none of the agents. Here we want to start with solving Nash Equilibria of general two person problems and then specify to the discussion of the game of chicken, which is symmetric and the payoff matrix for both players satisfy certain constraints we will mention later. Finally, we attempted to find the optimal strategy for the first player, considering Nash Equilibria and a game with objective of winning over the opponent. And we believe future studies in this field may take advantage of techniques like reinforcement learning.]

References

[1]

The Stanford Encyclopedia of Philosophy (2019), Game Theory, Game Theory (Stanford Encyclopedia of Philosophy)

Google Scholar

[2]

Robert J. Vanderbei (2014), Linear Programming: Foundations and Extensions, Springer Science+Business Media, New York

Crossref

Google Scholar

[3]

Joel N. Franklin (1980), Methods of Mathematical Economics, Springer-Verlag, New York

Google Scholar

[4]

John F. Nash (1950), Equilibrium Points in n-Person Games, National Academy of Sciences, Vol. 36, No. 1 (Jan. 15, 1950), pp. 48-49

Crossref

Google Scholar

[5]

Rowland, Todd and Weisstein, Eric W. "Antisymmetric Matrix." From MathWorld–A Wolfram Web Resource. https://mathworld.wolfram.com/AntisymmetricMatrix.html

Google Scholar

[6]

Howard E. Haber (2015), Notes on antisymmetric matrices and the pfaffian, pfaffian2.dvi (ucsc.edu)

Google Scholar

[7]

Ochs Jack (1995), Games with Unique, Mixed Strategy Equilibria: An Experimental Study, Games and Economic Behavior, Vol 10, No. 1, July 1995, pp. 202-217

Google Scholar

[8]

Jun Tanimoto, Hiroki Sagara (2007), Relationship between dilemma occurrence and the existence of a weakly dominant strategy in a two-player symmetric game, Biosystems, Vol 90, No. 1, July-August 2007, pp. 105-114

Crossref

Google Scholar

[9]

Xiaofeng Wang and Tuomas Sandholm (2002), Reinforcement Learning to Play an Optimal Nash Equilibrium in Team Markov Games, Reinforcement Learning to Play an Optimal Nash Equilibrium in Team Markov Games (nips.cc)

Google Scholar

[10]

Drew Fudenberg and David M. Kreps (1992), Learning Mixed Equilibria, Learning mixed equilibria (mit.edu)

Google Scholar

Recommendations

Expressiveness and Nash Equilibrium in Iterated Boolean Games
We define and investigate a novel notion of expressiveness for temporal logics that is based on game theoretic equilibria of multi-agent systems. We use iterated Boolean games as our abstract model of multi-agent systems [Gutierrez et al. 2013, 2015a]. In ...
Nash equilibria of discontinuous non-zero-sum two-person games
Abstract
The paper investigates two classes of non-zero-sum two-person games on the unit square, where the payoff function of Player 1 is convex or concave in the first variable. It is shown that this assumption together with the boundedness of payoff ...
Inapproximability of Nash Equilibrium
STOC '15: Proceedings of the forty-seventh annual ACM symposium on Theory of Computing

We prove that finding an ε-approximate Nash equilibrium is PPAD-complete for constant ε and a particularly simple class of games: polymatrix, degree 3 graphical games, in which each player has only two actions.

As corollaries, we also prove similar ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

ICIBE '21: Proceedings of the 7th International Conference on Industrial and Business Engineering

September 2021

411 pages

ISBN:9781450390644

DOI:10.1145/3494583

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 09 January 2022

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article
Research
Refereed limited

Conference

ICIBE 2021

ICIBE 2021: 2021 the 7th International Conference on Industrial and Business Engineering

September 27 - 29, 2021

Macau, China

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

0
Total Citations
42
Total Downloads

Downloads (Last 12 months)19
Downloads (Last 6 weeks)0

Reflects downloads up to 20 Sep 2024

Other Metrics

View Author Metrics

Citations

View Options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

HTML Format

View this article in HTML Format.

HTML Format

Abstract

References

Recommendations

Expressiveness and Nash Equilibrium in Iterated Boolean Games

Nash equilibria of discontinuous non-zero-sum two-person games

Inapproximability of Nash Equilibrium

Comments

Information

Published In

Publisher

Publication History

Permissions

Check for updates

Author Tags

Qualifiers

Conference

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Get Access

Login options

Full Access

View options

PDF

eReader

HTML Format

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations