Approximation algorithms for indefinite quadratic programming
Mathematical Programming: Series A and B
Random walks and an O*(n5) volume algorithm for convex bodies
Random Structures & Algorithms
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
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
Computing equilibria in multi-player games
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Nash Equilibria in Random 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
A technique for reducing normal-form games to compute a Nash equilibrium
AAMAS '06 Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems
On the complexity of Nash equilibria of action-graph games
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
An Efficient PTAS for Two-Strategy Anonymous Games
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Settling the complexity of computing two-player Nash equilibria
Journal of the ACM (JACM)
A note on approximate Nash equilibria
Theoretical Computer Science
Algorithmic Game Theory: A Snapshot
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Algorithms for playing games with limited randomness
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Exploiting concavity in bimatrix games: new polynomially tractable subclasses
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Practical and efficient approximations of nash equilibria for win-lose games based on graph spectra
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Rank-1 bimatrix games: a homeomorphism and a polynomial time algorithm
Proceedings of the forty-third annual ACM symposium on Theory of computing
Parameterized two-player nash equilibrium
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Survey: Nash equilibria: Complexity, symmetries, and approximation
Computer Science Review
Efficient algorithms for constant well supported approximate equilibria in bimatrix games
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
The approximate rank of a matrix and its algorithmic applications: approximate rank
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We propose and investigate bimatrix games, whose (entry-wise) sum of the pay-off matrices of the two players is of rank k, where k is a constant. We will say the rank of such a game is k. For every fixed k, the class of rank k-games strictly generalizes the class of zero-sum games, but is a very special case of general bimatrix games. We show that even for k = 1 the set of Nash equilibria of these games can consist of an arbitrarily large number of connected components. While the question of exact polynomial time algorithms to find a Nash equilibrium remains open for games of fixed rank, we can provide a deterministic polynomial time algorithm for finding an ε-approximation (whose running time is polynomial in 1\ε) as well as a randomized polynomial time approximation algorithm (whose running time is similar), but which offers the possibility of finding an exact solution in polynomial time if a conjecture is valid. The latter algorithm is based on a new application of random sampling methods to quadratic optimization problems of fixed rank.