Communications of the ACM
Ranking games that have competitiveness-based strategies
Proceedings of the 11th ACM conference on Electronic commerce
Local search: simple, successful, but sometimes sluggish
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
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
How do you like your equilibrium selection problems? hard, or very hard?
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Mixing time and stationary expected social welfare of logit dynamics
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
On nash-equilibria of approximation-stable games
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
A direct reduction from k-player to 2-player approximate nash equilibrium
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
On the Complexity of Nash Equilibria and Other Fixed Points
SIAM Journal on Computing
Market equilibrium under separable, piecewise-linear, concave utilities
Journal of the ACM (JACM)
Complexity and economics: computational constraints may not matter empirically
ACM SIGecom Exchanges
A revealed preference approach to computational complexity in economics
Proceedings of the 12th ACM conference on Electronic commerce
Repeated matching pennies with limited randomness
Proceedings of the 12th ACM conference on Electronic commerce
Approximability of symmetric bimatrix games and related experiments
SEA'11 Proceedings of the 10th international conference on Experimental algorithms
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Automatizability and simple stochastic games
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
The complexity of nash equilibria in limit-average games
CONCUR'11 Proceedings of the 22nd international conference on Concurrency theory
On the approximation performance of fictitious play in finite games
ESA'11 Proceedings of the 19th European conference on Algorithms
Complexity of rational and irrational Nash equilibria
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
How Hard Is It to Approximate the Best Nash Equilibrium?
SIAM Journal on Computing
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Metastability of logit dynamics for coordination games
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Modeling internet security investments: tackling topological information uncertainty
GameSec'11 Proceedings of the Second international conference on Decision and Game Theory for Security
Economic models for cloud service markets
ICDCN'12 Proceedings of the 13th international conference on Distributed Computing and Networking
On mutual concavity and strategically-zero-sum bimatrix games
Theoretical Computer Science
The Computational Complexity of Nash Equilibria in Concisely Represented Games
ACM Transactions on Computation Theory (TOCT)
Intrinsic robustness of the price of anarchy
Communications of the ACM
Bayesian optimal auctions via multi- to single-agent reduction
Proceedings of the 13th ACM Conference on Electronic Commerce
Lossy stochastic game abstraction with bounds
Proceedings of the 13th ACM Conference on Electronic Commerce
On envy-free pareto efficient pricing
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
The complexity of decision problems about nash equilibria in win-lose games
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
Approximate well-supported nash equilibria below two-thirds
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
On the communication complexity of approximate nash equilibria
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
The Complexity of the Homotopy Method, Equilibrium Selection, and Lemke-Howson Solutions
ACM Transactions on Economics and Computation - Special Issue on Algorithmic Game Theory
Learning equilibria of games via payoff queries
Proceedings of the fourteenth ACM conference on Electronic commerce
The empirical implications of rank in Bimatrix games
Proceedings of the fourteenth ACM conference on Electronic commerce
On the Complexity of Approximating a Nash Equilibrium
ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
On the complexity of trial and error
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
The complexity of non-monotone markets
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Economic models for cloud service markets: Pricing and Capacity planning
Theoretical Computer Science
Full characterization of quantum correlated equilibria
Quantum Information & Computation
Game-theoretic question selection for tests
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Computational Aspects of Uncertainty Profiles and Angel-Daemon Games
Theory of Computing Systems
Complexity of Rational and Irrational Nash Equilibria
Theory of Computing Systems
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In 1951, John F. Nash proved that every game has a Nash equilibrium [Ann. of Math. (2), 54 (1951), pp. 286-295]. His proof is nonconstructive, relying on Brouwer's fixed point theorem, thus leaving open the questions, Is there a polynomial-time algorithm for computing Nash equilibria? And is this reliance on Brouwer inherent? Many algorithms have since been proposed for finding Nash equilibria, but none known to run in polynomial time. In 1991 the complexity class PPAD (polynomial parity arguments on directed graphs), for which Brouwer's problem is complete, was introduced [C. Papadimitriou, J. Comput. System Sci., 48 (1994), pp. 489-532], motivated largely by the classification problem for Nash equilibria; but whether the Nash problem is complete for this class remained open. In this paper we resolve these questions: We show that finding a Nash equilibrium in three-player games is indeed PPAD-complete; and we do so by a reduction from Brouwer's problem, thus establishing that the two problems are computationally equivalent. Our reduction simulates a (stylized) Brouwer function by a graphical game [M. Kearns, M. Littman, and S. Singh, Graphical model for game theory, in 17th Conference in Uncertainty in Artificial Intelligence (UAI), 2001], relying on “gadgets,” graphical games performing various arithmetic and logical operations. We then show how to simulate this graphical game by a three-player game, where each of the three players is essentially a color class in a coloring of the underlying graph. Subsequent work [X. Chen and X. Deng, Setting the complexity of 2-player Nash-equilibrium, in 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS), 2006] established, by improving our construction, that even two-player games are PPAD-complete; here we show that this result follows easily from our proof.