Algorithms, games, and the internet
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ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Playing large games using simple strategies
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Nash Equilibria in Random Games
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Reducibility among equilibrium problems
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The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
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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
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Complexity results about Nash equilibria
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WINE'06 Proceedings of the Second 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
Efficient algorithms for constant well supported approximate equilibria in bimatrix games
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Approximate Equilibria for Strategic Two Person Games
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Probabilistic techniques in algorithmic game theory
SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
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We study the existence and tractability of a notion of approximate equilibria in bimatrix games, called well supported approximate Nash Equilibria (SuppNE in short).We prove existence of e-SuppNE for any constant e ? (0, 1), with only logarithmic support sizes for both players. Also we propose a polynomial-time construction of SuppNE, both for win lose and for arbitrary (normalized) bimatrix games. The quality of these SuppNE depends on the girth of the Nash Dynamics graph in the win lose game, or a (rounded-off) win lose image of the original normalized game. Our constructions are very successful in sparse win lose games (ie, having a constant number of (0, 1)-elements in the bimatrix) with large girth in the Nash Dynamics graph. The same holds also for normalized games whose win lose image is sparse with large girth. Finally we prove the simplicity of constructing SuppNE both in random normalized games and in random win lose games. In the former case we prove that the uniform full mix is an o(1)-SuppNE, while in the case of win lose games, we show that (with high probability) there is either a PNE or a 0.5-SuppNE with support sizes only 2.