Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
On the complexity of the parity argument and other inefficient proofs of existence
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
A game-theoretic classification of interactive complexity classes
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Exponentially Many Steps for Finding a Nash Equilibrium in a Bimatrix Game
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Computing correlated equilibria in multi-player games
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On the Complexity of Succinct Zero-Sum Games
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Reducibility among equilibrium problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Graphical models for game theory
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
The Search for Equilibrium Concepts
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
On the complexity of Nash equilibria of action-graph games
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Computing pure strategy nash equilibria in compact symmetric games
Proceedings of the 11th ACM conference on Electronic commerce
A direct reduction from k-player to 2-player approximate nash equilibrium
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
On the Complexity of Nash Equilibria and Other Fixed Points
SIAM Journal on Computing
Equilibria problems on games: Complexity versus succinctness
Journal of Computer and System Sciences
Making economic theory operational
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
A general framework for computing optimal correlated equilibria in compact games
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
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A recent sequence of results established that computing Nash equilibria in normal form games is a PPAD-complete problem even in the case of two players [11,6,4]. By extending these techniques we prove a general theorem, showing that, for a far more general class of families of succinctly representable multiplayer games, the Nash equilibrium problem can also be reduced to the two-player case. In view of empirically successful algorithms available for this problem, this is in essence a positive result — even though, due to the complexity of the reductions, it is of no immediate practical significance. We further extend this conclusion to extensive form games and network congestion games, two classes which do not fall into the same succinct representation framework, and for which no positive algorithmic result had been known.