Playing large games using simple strategies
Proceedings of the 4th ACM conference on Electronic commerce
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
A new polynomial-time algorithm for linear programming
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Communication complexity as a lower bound for learning in games
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Some Discriminant-Based PAC Algorithms
The Journal of Machine Learning Research
Settling the complexity of computing two-player Nash equilibria
Journal of the ACM (JACM)
The Complexity of Computing a Nash Equilibrium
SIAM Journal on Computing
New algorithms for approximate Nash equilibria in bimatrix games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
An optimization approach for approximate Nash equilibria
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
A note on approximate nash equilibria
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Learning equilibria of games via payoff queries
Proceedings of the fourteenth ACM conference on Electronic commerce
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We study the problem of computing approximate Nash equilibria, in a setting where players initially know their own payoffs but not the payoffs of other players. In order for a solution of reasonable quality to be found, some amount of communication needs to take place between the players. We are interested in algorithms where the communication is substantially less than the contents of a payoff matrix, for example logarithmic in the size of the matrix. At one extreme is the case where the players do not communicate at all; for this case (with 2 players having n×n matrices) ε-Nash equilibria can be computed for ε=3/4, while there is a lower bound of slightly more than 1/2 on the lowest ε achievable. When the communication is polylogarithmic in n, we show how to obtain ε=0.438. For one-way communication we show that ε=1/2 is the exact answer.