Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Existence of correlated equilibria
Mathematics of Operations Research
Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
Journal of Symbolic Computation
The Structure and Complexity of Nash Equilibria for a Selfish Routing Game
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Graphical Models for Game Theory
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Correlated equilibria in graphical games
Proceedings of the 4th ACM conference on Electronic commerce
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Selfish caching in distributed systems: a game-theoretic analysis
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
The Price of Stability for Network Design with Fair Cost Allocation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Algorithm Design
On the Complexity of Succinct Zero-Sum Games
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The computational complexity of nash equilibria in concisely represented games
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Prediction, Learning, and Games
Prediction, Learning, and Games
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Symmetries and the complexity of pure Nash equilibrium
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
The complexity of games on highly regular graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Computing an Extensive-Form Correlated Equilibrium in Polynomial Time
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Intrinsic robustness of the price of anarchy
Proceedings of the forty-first annual ACM symposium on Theory of computing
ADT '09 Proceedings of the 1st International Conference on Algorithmic Decision Theory
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Mediated Equilibria in Load-Balancing Games
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Computing pure strategy nash equilibria in compact symmetric games
Proceedings of the 11th ACM conference on Electronic commerce
Polynomial computation of exact correlated equilibrium in compact games
ACM SIGecom Exchanges
Polynomial-time computation of exact correlated equilibrium in compact games
Proceedings of the 12th ACM conference on Electronic commerce
Equilibria problems on games: Complexity versus succinctness
Journal of Computer and System Sciences
Reaching correlated equilibria through multi-agent learning
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
The Knowledge Engineering Review
A general framework for computing optimal correlated equilibria in compact games
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
Computing nash equilibria of action-graph games via support enumeration
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
A multi-agent prediction market based on partially observable stochastic game
Proceedings of the 13th International Conference on Electronic Commerce
Computing pure Bayesian-Nash equilibria in games with finite actions and continuous types
Artificial Intelligence
Proceedings of the 2nd ACM international conference on High confidence networked systems
Scaling-up security games with boundedly rational adversaries: a cutting-plane approach
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Decentralized anti-coordination through multi-agent learning
Journal of Artificial Intelligence Research
Computational Aspects of Uncertainty Profiles and Angel-Daemon Games
Theory of Computing Systems
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We develop polynomial-time algorithms for finding correlated equilibria—a well-studied notion of rationality that generalizes the Nash equilibrium—in a broad class of succinctly representable multiplayer games, encompassing graphical games, anonymous games, polymatrix games, congestion games, scheduling games, local effect games, as well as several generalizations. Our algorithm is based on a variant of the existence proof due to Hart and Schmeidler, and employs linear programming duality, the ellipsoid algorithm, Markov chain steady state computations, as well as application-specific methods for computing multivariate expectations over product distributions. For anonymous games and graphical games of bounded tree-width, we provide a different polynomial-time algorithm for optimizing an arbitrary linear function over the set of correlated equilibria of the game. In contrast to our sweeping positive results for computing an arbitrary correlated equilibrium, we prove that optimizing over correlated equilibria is NP-hard in all of the other classes of games that we consider.