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
Computers and Intractability: A Guide to the Theory of NP-Completeness
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Graphical Models for Game Theory
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Playing large games using simple strategies
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Reducibility among equilibrium problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The complexity of computing a Nash equilibrium
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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
The communication complexity of uncoupled nash equilibrium procedures
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On the Complexity of Nash Equilibria and Other Fixed Points (Extended Abstract)
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
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Complexity results about Nash equilibria
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IEEE Transactions on Information Theory
Algorithms for closed under rational behavior (CURB) sets
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SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
OREN: Optimal revocations in ephemeral networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
Graph transduction as a non-cooperative game
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The equivalence of sampling and searching
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Neural Computation
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WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Identification and application of Extract Class refactorings in object-oriented systems
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A game theoretical method for auto-scaling of multi-tiers web applications in cloud
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ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
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How long does it take until economic agents converge to an equilibrium? By studying the complexity of the problem of computing a mixed Nash equilibrium in a game, we provide evidence that there are games in which convergence to such an equilibrium takes prohibitively long. Traditionally, computational problems fall into two classes: those that have a polynomial-time algorithm and those that are NP-hard. However, the concept of NP-hardness cannot be applied to the rare problems where "every instance has a solution"---for example, in the case of games Nash's theorem asserts that every game has a mixed equilibrium (now known as the Nash equilibrium, in honor of that result). We show that finding a Nash equilibrium is complete for a class of problems called PPAD, containing several other known hard problems; all problems in PPAD share the same style of proof that every instance has a solution.