Playing large games using simple strategies
Proceedings of the 4th ACM conference on Electronic commerce
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
On the Complexity of Two-PlayerWin-Lose Games
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Computing Nash Equilibria: Approximation and Smoothed Complexity
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Progress in approximate nash equilibria
Proceedings of the 8th ACM conference on Electronic commerce
Efficient computation of nash equilibria for very sparse win-lose bimatrix games
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
The approximation complexity of win-lose games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Simple search methods for finding a Nash equilibrium
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Mixed-integer programming methods for finding Nash equilibria
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
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
Polynomial algorithms for approximating nash equilibria of bimatrix games
WINE'06 Proceedings of the Second 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
Hi-index | 0.00 |
The problem of computing a Nash equilibrium in a normal form 2-player game (or bimatrix games) is PPAD-complete in general, while it can be efficiently solved in a special subclass which we call regular bimatrix games. The current best approximation algorithm, proposed in [19], achieves a guarantee of 0.3393. In this paper we design a polynomial time algorithm for computing exact and approximate Nash equilibria for bimatrix games. The novelty of this contribution is twofold. For regular bimatrix games, it allows to compute equilibria whose payoffs optimize any objective function and meet any set of constraints which can be expressed through linear programming, while, in the general case, it computes α-approximate Nash equilibria, where α is the maximum difference between any two payoffs in the same strategy of any player. Hence, our algorithm improves the best know approximation guarantee for the bimatrices in which α