Article

Correlated equilibria in graphical games

Authors:

Michael Kearns,

Luis OrtizAuthors Info & Claims

EC '03: Proceedings of the 4th ACM conference on Electronic commerce

Pages 42 - 47

https://doi.org/10.1145/779928.779934

Published: 09 June 2003 Publication History

Abstract

We examine correlated equilibria in the recently introduced formalism of graphical games, a succinct representation for multiplayer games. We establish a natural and powerful relationship between the graphical structure of a multiplayer game and a certain Markov network representing distributions over joint actions. Our first main result establishes that this Markov network succinctly represents all correlated equilibria of the graphical game up to expected payoff equivalence. Our second main result provides a general algorithm for computing correlated equilibria in a graphical game based on its associated Markov network. For a special class of graphical games that includes trees, this algorithm runs in time polynomial in the graphical game representation (which is polynomial in the number of players and exponential in the graph degree).

References

[1]

R.J. Aumann. Subjectivity and correlation in randomized strategies. Journal of Mathematical Economics, 1, 1974.

[2]

R.J. Aumann. Correlated equilibrium as an expression of Bayesian rationality. Econometrica, 55, 1987.

[3]

A. Berger, S. Della Pietra, and V. Della Pietra. A maximum entropy approach to natural language processing. Computational Linguistics, 22penalty0 (1), March 1996.

Digital Library

[4]

A. P. Dawid and S. L. Lauritzen. Hyper Markov laws in the statistical analysis of decomposable graphical models. The Annals of Statistics, 21penalty0 (3):penalty0 1271--1317, September 1993.

[5]

M. Dyer, A. Frieze, and R. Kannan. A random polynomial time algorithm for approximating the volume of a convex body. JACM, 38penalty0 (1):penalty0 1--17, 1991.

Digital Library

[6]

D. Foster and R. Vohra. Calibrated learning and correlated equilibrium. Games and Economic Behavior, 1997.

[7]

D. Foster and R. Vohra. Regret in the on-line decision problem. Games and Economic Behavior, pages 7--36, 1999.

[8]

M. Kearns, M. Littman, and S. Singh. Graphical models for game theory. In Proceedings of the Conference on Uncertainty in Artificial Intelligence, pages 253--260, 2001.

Digital Library

[9]

Daphne Koller and Brian Milch. Multi-agent influence diagrams for representing and solving games. Games and Economic Behavior. To appear.

[10]

P. La Mura. Game networks. In Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence (UAI), pages 335--342, 2000.

Digital Library

[11]

M. Littman, M. Kearns, and S. Singh. An efficient exact algorithm for singly connected graphical games. In Neural Information Processing Systems, 2002.

[12]

J. F. Nash. Non-cooperative games. Annals of Mathematics, 54:penalty0 286--295, 1951.

[13]

L. Ortiz and M. Kearns. Nash propagation for loopy graphical games. In Neural Information Processing Systems, 2003. To appear.

[14]

G. Owen. Game Theory. Academic Press, UK, 1995.

[15]

J. Pearl. Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann, 1988.

Digital Library

[16]

D. Vickrey and D. Koller. Multi-agent algorithms for solving graphical games. In Proceedings of the National Conference on Artificial Intelligence (AAAI), 2002.

Digital Library

Cited By

Arditti LComo GFagnani F(2024)On the Separability of Functions and GamesIEEE Transactions on Control of Network Systems10.1109/TCNS.2023.331455211:2(831-841)Online publication date: Jun-2024
https://doi.org/10.1109/TCNS.2023.3314552
Pipis CFarina GOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Polynomial-time linear-swap regret minimization in imperfect-information sequential gamesProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3667350(28255-28280)Online publication date: 10-Dec-2023
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Farina GCelli AMarchesi AGatti N(2022)Simple Uncoupled No-regret Learning Dynamics for Extensive-form Correlated EquilibriumJournal of the ACM10.1145/356377269:6(1-41)Online publication date: 18-Nov-2022
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Index Terms

Correlated equilibria in graphical games
1. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Conferences

EC '03: Proceedings of the 4th ACM conference on Electronic commerce

June 2003

292 pages

ISBN:158113679X

DOI:10.1145/779928

General Chair:
Danny Menasce
George Mason University
,
Program Chair:
Noam Nisan
Hebrew University of Jerusalem

Copyright © 2003 ACM.

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Published: 09 June 2003

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EC03: The Fourth ACM Conference on Electronic Commerce

June 9 - 12, 2003

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EC '03 Paper Acceptance Rate 21 of 110 submissions, 19%;

Overall Acceptance Rate 664 of 2,389 submissions, 28%

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Cited By

Arditti LComo GFagnani F(2024)On the Separability of Functions and GamesIEEE Transactions on Control of Network Systems10.1109/TCNS.2023.331455211:2(831-841)Online publication date: Jun-2024
https://doi.org/10.1109/TCNS.2023.3314552
Pipis CFarina GOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Polynomial-time linear-swap regret minimization in imperfect-information sequential gamesProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3667350(28255-28280)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3666122.3667350
Farina GCelli AMarchesi AGatti N(2022)Simple Uncoupled No-regret Learning Dynamics for Extensive-form Correlated EquilibriumJournal of the ACM10.1145/356377269:6(1-41)Online publication date: 18-Nov-2022
https://dl.acm.org/doi/10.1145/3563772
Fernando MSenanayake RSwany M(2022)CoCo Games: Graphical Game-Theoretic Swarm Control for Communication-Aware CoverageIEEE Robotics and Automation Letters10.1109/LRA.2022.31609687:3(5966-5973)Online publication date: Jul-2022
https://doi.org/10.1109/LRA.2022.3160968
Barik AHonorio J(2022)Provable Sample Complexity Guarantees For Learning Of Continuous-Action Graphical Games With Nonparametric UtilitiesICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)10.1109/ICASSP43922.2022.9747045(4443-4447)Online publication date: 23-May-2022
https://doi.org/10.1109/ICASSP43922.2022.9747045
García Cabello JCastillo PAguilar-Luzon MChiclana FHerrera-Viedma E(2021)A Methodology for Redesigning Networks by Using Markov Random FieldsMathematics10.3390/math91213899:12(1389)Online publication date: 15-Jun-2021
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Zhang KYang ZLiu HZhang TBasar T(2021)Finite-Sample Analysis for Decentralized Batch Multiagent Reinforcement Learning With Networked AgentsIEEE Transactions on Automatic Control10.1109/TAC.2021.304934566:12(5925-5940)Online publication date: Dec-2021
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Adkins RMount DZhang A(2019)A Game-Theoretic Approach for Minimizing Delays in Autonomous IntersectionsTraffic and Granular Flow '1710.1007/978-3-030-11440-4_16(131-139)Online publication date: 24-Oct-2019
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Foley MForber PSmead RRiedl C(2018)Conflict and convention in dynamic networksJournal of The Royal Society Interface10.1098/rsif.2017.083515:140(20170835)Online publication date: 21-Mar-2018
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Kearns M(2018)Graphical GamesThe New Palgrave Dictionary of Economics10.1057/978-1-349-95189-5_2123(5432-5436)Online publication date: 15-Feb-2018
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