research-article

On the Complexity of Nash Equilibria in Anonymous Games

Authors:

Xi Chen,

David Durfee,

Anthi OrfanouAuthors Info & Claims

STOC '15: Proceedings of the forty-seventh annual ACM symposium on Theory of Computing

Pages 381 - 390

https://doi.org/10.1145/2746539.2746571

Published: 14 June 2015 Publication History

Get Access

Abstract

We show that the problem of finding an ε-approximate Nash equilibrium in an {anonymous} game with seven pure strategies is complete in PPAD, when the approximation parameter ε is exponentially small in the number of players.

References

[1]

H. Ackermann, H. Röglin, and B. Vöcking. On the impact of combinatorial structure on congestion games. Journal of the ACM, 55:1--22, 2008.

Digital Library

Google Scholar

[2]

Y. Azrieli and E. Shmaya. Lipschitz games. Mimeo, Ohio State University, 2011.

Google Scholar

[3]

Y. Babichenko. Best-reply dynamics in large binary-choice anonymous games. Games and Economic Behavior, 81:130--144, 2013.

Crossref

Google Scholar

[4]

M. Blonski. Anonymous games with binary actions. Games and Economic Behavior, pages 171--180, 1999.

Crossref

Google Scholar

[5]

M. Blonski. The women of Cairo: Equilibria in large anonymous games. Journal of Mathematical Economics, pages 254--263, 2005.

Google Scholar

[6]

F. Brandt, F. Fischer, and M. Holzer. Symmetries and the complexity of pure Nash equilibrium. Journal of Computer and System Sciences, 75(3):163--177, 2009.

Digital Library

Google Scholar

[7]

Y. Cai and C. Daskalakis. On minmax theorems for multiplayer games. In Proceedings of the 22nd ACM-SIAM Symposium on Discrete Algorithms, pages 217--234, 2011.

Digital Library

Google Scholar

[8]

I. Caragiannis, A. Fanelli, N. Gravin, and A. Skopalik. Efficient computation of approximate pure Nash equilibria in congestion games. In Proceedings of the 52nd Annual IEEE Symposium on Foundations of Computer Science, pages 532--541, 2011.

Digital Library

Google Scholar

[9]

I. Caragiannis, A. Fanelli, N. Gravin, and A. Skopalik. Approximate pure Nash equilibria in weighted congestion games: existence, efficient computation, and structure. In Proceedings of the 13th ACM Conference on Electronic Commerce, 2012.

Digital Library

Google Scholar

[10]

X. Chen, X. Deng, and S.-H. Teng. Settling the complexity of computing two-player Nash equilibria. Journal of the ACM, 56(3):1--57, 2009.

Digital Library

Google Scholar

[11]

X. Chen, D. Durfee, and A. Orfanou. On the complexity of Nash equilibria in anonymous games. CoRR, abs/1412.5681, 2014.

Google Scholar

[12]

X. Chen, D. Paparas, and M. Yannakakis. The complexity of non-monotone markets. In Proceedings of the 45th Annual ACM Symposium on Theory of Computing, pages 181--190, 2013.

Digital Library

Google Scholar

[13]

S. Chien and A. Sinclair. Convergence to approximate Nash equilibria in congestion games. Games and Economic Behavior, 71(2):315--327, 2011.

Crossref

Google Scholar

[14]

C. Daskalakis. An efficient PTAS for two-strategy anonymous games. In Proceedings of the 4th International Workshop on Internet and Network Economics, pages 186--197, 2008.

Digital Library

Google Scholar

[15]

C. Daskalakis, P. Goldberg, and C. Papadimitriou. The complexity of computing a Nash equilibrium. SIAM Journal on Computing, 39(1), 2009.

Digital Library

Google Scholar

[16]

C. Daskalakis and C. Papadimitriou. Computing equilibria in anonymous games. In Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science, pages 83--93, 2007.

Digital Library

Google Scholar

[17]

C. Daskalakis and C. Papadimitriou. Discretized multinomial distributions and Nash equilibria in anonymous games. In Proceedings of the 49th Annual IEEE Symposium on Foundations of Computer Science, pages 25--34, 2008.

Digital Library

Google Scholar

[18]

C. Daskalakis and C. Papadimitriou. On oblivious PTAS's for Nash equilibrium. In Proceedings of the 41st Annual ACM Symposium on Theory of Computing, pages 75--84, 2009.

Digital Library

Google Scholar

[19]

C. Daskalakis and C. Papadimitriou. Approximate Nash equilibria in anonymous games. Journal of Economic Theory, 2014.

Google Scholar

[20]

C. Daskalakis and C. H. Papadimitriou. Sparse covers for sums of indicators. CoRR, abs/1306.1265, 2013.

Google Scholar

[21]

J. Ely and W. Sandholm. Evolution in Bayesian games I. Theory of Games and Economic Behavior, 53:83--109, 2005.

Crossref

Google Scholar

[22]

A. Fabrikant, C. Papadimitriou, and K. Talwar. The complexity of pure Nash equilibria. In Proceedings of the 36th Annual ACM Symposium on Theory of Computing, pages 604--612, 2004.

Digital Library

Google Scholar

[23]

P. W. Goldberg and S. Turchetta. Query complexity of approximate equilibria in anonymous games. CoRR, abs/1412.6455, 2014.

Google Scholar

[24]

C. Holt and A. Roth. The Nash equilibrium: A perspective. Proceedings of the National Academy of Sciences, 101(12):3999--4002, 2004.

Crossref

Google Scholar

[25]

E. Kalai. Partially-specified large games. Proceedings of the 1st International Workshop on Internet and Network Economics, pages 3--13, 2005.

Digital Library

Google Scholar

[26]

I. Milchtaich. Congestion games with player-specific payoff functions. Games and Economic Behavior, pages 111--124, 1996.

Crossref

Google Scholar

[27]

J. Nash. Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 36(1):48--49, 1950.

Crossref

Google Scholar

[28]

J. Nash. Non-cooperative games. Annals of Mathematics, 54(2):286--295, 1951.

Crossref

Google Scholar

[29]

C. Papadimitriou and T. Roughgarden. Computing correlated equilibria in multi-player games. Journal of the ACM, 55(3):1--29, 2008.

Digital Library

Google Scholar

[30]

S. Rashid. Equilibrium points of nonatomic games: Asymptotic results. Economics Letters, 12:7--10, 1983.

Crossref

Google Scholar

[31]

R. Rosenthal. A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory, 2(1):65--67, 1973.

Digital Library

Google Scholar

[32]

A. Rubinstein. Inapproximability of Nash equilibrium. In Proceedings of the 47th ACM Symposium on Theory of Computing, 2015.

Digital Library

Google Scholar

[33]

D. Schmeidler. Equilibrium points of nonatomic games. Journal of Statistical Physics, 7(4):295--300, 1973.

Crossref

Google Scholar

[34]

A. Skopalik and B. Vöcking. Inapproximability of pure Nash equilibria. In Proceedings of the 40th Annual ACM Symposium on Theory of Computing, pages 355--364, 2008.

Digital Library

Google Scholar

Cited By

View all

Deligkas AFearnley JHollender AMelissourgos T(2024)Pure-Circuit: Tight Inapproximability for PPADJournal of the ACM10.1145/367816671:5(1-48)Online publication date: 15-Jul-2024
https://dl.acm.org/doi/10.1145/3678166
Göös MHollender AJain SMaystre GPires WRobere RTao R(2024)Separations in Proof Complexity and TFNPJournal of the ACM10.1145/366375871:4(1-45)Online publication date: 9-May-2024
https://dl.acm.org/doi/10.1145/3663758
Chen XPeng BSaha BServedio R(2023)Complexity of Equilibria in First-Price Auctions under General Tie-Breaking RulesProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585195(698-709)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585195
Show More Cited By

Index Terms

On the Complexity of Nash Equilibria in Anonymous Games
1. Theory of computation
  1. Design and analysis of algorithms

Recommendations

Settling the complexity of computing two-player Nash equilibria

We prove that Bimatrix, the problem of finding a Nash equilibrium in a two-player game, is complete for the complexity class PPAD (Polynomial Parity Argument, Directed version) introduced by Papadimitriou in 1991.

Our result, building upon the work of ...
Computing Approximate Nash Equilibria in Polymatrix Games

In an $$\epsilon $$∈-Nash equilibrium, a player can gain at most $$\epsilon $$∈ by unilaterally changing his behavior. For two-player (bimatrix) games with payoffs in [0, 1], the best-known $$\epsilon $$∈ achievable in polynomial time is 0.3393 (...
Multi-player Approximate Nash Equilibria
AAMAS '17: Proceedings of the 16th Conference on Autonomous Agents and MultiAgent Systems

In this paper we study the complexity of finding approximate Nash equilibria in multi-player normal-form games. First, for any constant number m, we present a polynomial-time algorithm for computing a relative (1 - 1(1+(m-1)^m))-Nash equilibrium in ...

Comments

Information & Contributors

Information

Published In

STOC '15: Proceedings of the forty-seventh annual ACM symposium on Theory of Computing

June 2015

916 pages

ISBN:9781450335362

DOI:10.1145/2746539

General Chair:
Rocco Servedio
Columbia University
,
Program Chair:
Ronitt Rubinfeld
MIT and Tel Aviv University

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 the author(s) 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: 14 June 2015

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Funding Sources

National Science Foundation

Conference

STOC '15

Sponsor:

SIGACT

STOC '15: Symposium on Theory of Computing

June 14 - 17, 2015

Oregon, Portland, USA

Acceptance Rates

STOC '15 Paper Acceptance Rate 93 of 347 submissions, 27%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

Upcoming Conference

STOC '25

Sponsor:
sigact

57th Annual ACM Symposium on Theory of Computing (STOC 2025)

June 23 - 27, 2025

Prague , Czech Republic

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

16
Total Citations
View Citations
265
Total Downloads

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

Reflects downloads up to 12 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

View all

Deligkas AFearnley JHollender AMelissourgos T(2024)Pure-Circuit: Tight Inapproximability for PPADJournal of the ACM10.1145/367816671:5(1-48)Online publication date: 15-Jul-2024
https://dl.acm.org/doi/10.1145/3678166
Göös MHollender AJain SMaystre GPires WRobere RTao R(2024)Separations in Proof Complexity and TFNPJournal of the ACM10.1145/366375871:4(1-45)Online publication date: 9-May-2024
https://dl.acm.org/doi/10.1145/3663758
Chen XPeng BSaha BServedio R(2023)Complexity of Equilibria in First-Price Auctions under General Tie-Breaking RulesProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585195(698-709)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585195
Papadimitriou CPeng B(2023)Public goods games in directed networksGames and Economic Behavior10.1016/j.geb.2023.02.002139(161-179)Online publication date: May-2023
https://doi.org/10.1016/j.geb.2023.02.002
Filos-Ratsikas AGoldberg P(2022)The Complexity of Necklace Splitting, Consensus-Halving, and Discrete Ham SandwichSIAM Journal on Computing10.1137/20M131267852:2(STOC19-200-STOC19-268)Online publication date: 28-Feb-2022
https://doi.org/10.1137/20M1312678
Goos MHollender AJain SMaystre GPires WRobere RTao R(2022)Separations in Proof Complexity and TFNP2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS54457.2022.00111(1150-1161)Online publication date: Oct-2022
https://doi.org/10.1109/FOCS54457.2022.00111
Deligkas AFearnley JHollender AMelissourgos T(2022)Pure-Circuit: Strong Inapproximability for PPAD2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS54457.2022.00022(159-170)Online publication date: Oct-2022
https://doi.org/10.1109/FOCS54457.2022.00022
Papadimitriou CPeng BBiró PChawla SEchenique F(2021)Public Goods Games in Directed NetworksProceedings of the 22nd ACM Conference on Economics and Computation10.1145/3465456.3467616(745-762)Online publication date: 18-Jul-2021
https://dl.acm.org/doi/10.1145/3465456.3467616
Babichenko YRubinstein AKhuller SVassilevska Williams V(2021)Settling the complexity of Nash equilibrium in congestion gamesProceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing10.1145/3406325.3451039(1426-1437)Online publication date: 15-Jun-2021
https://dl.acm.org/doi/10.1145/3406325.3451039
Babichenko YRubinstein A(2020)Communication complexity of Nash equilibrium in potential games (extended abstract)2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS46700.2020.00137(1439-1445)Online publication date: Nov-2020
https://doi.org/10.1109/FOCS46700.2020.00137
Show More Cited By

View Options

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

Abstract

References

Cited By

Index Terms

Recommendations

Settling the complexity of computing two-player Nash equilibria

Computing Approximate Nash Equilibria in Polymatrix Games

Multi-player Approximate Nash Equilibria

Comments

Information

Published In

Sponsors

Publisher

Publication History

Permissions

Check for updates

Author Tags

Qualifiers

Funding Sources

Conference

Acceptance Rates

Upcoming Conference

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

Login options

Full Access

View options

PDF

eReader

Share

Share this Publication link

Share on social media

Affiliations