Expressing combinatorial optimization problems by linear programs
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Lower bounds for non-commutative computation
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
The Quantum Communication Complexity of Sampling
SIAM Journal on Computing
A new protocol and lower bounds for quantum coin flipping
Journal of Computer and System Sciences - STOC 2001
Consequences and Limits of Nonlocal Strategies
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Communication complexity as a lower bound for learning in games
ICML '04 Proceedings of the twenty-first international conference on Machine learning
An information statistics approach to data stream and communication complexity
Journal of Computer and System Sciences - Special issue on FOCS 2002
Quantum Speed-Up of Markov Chain Based Algorithms
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
How Well Do People Play a Quantum Prisoner's Dilemma?
Quantum Information Processing
Toward a general theory of quantum games
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Entangled Games are Hard to Approximate
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Settling the complexity of computing two-player Nash equilibria
Journal of the ACM (JACM)
Parallel Approximation of Non-interactive Zero-sum Quantum Games
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
The Complexity of Computing a Nash Equilibrium
SIAM Journal on Computing
The communication complexity of correlation
IEEE Transactions on Information Theory
No Strong Parallel Repetition with Entangled and Non-signaling Provers
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
Nonnegative matrix factorization with bounded total variational regularization for face recognition
Pattern Recognition Letters
The Complexity of Distributions
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Unique Games with Entangled Provers Are Easy
SIAM Journal on Computing
The quantum monty hall problem
Quantum Information & Computation
Full characterization of quantum correlated equilibria
Quantum Information & Computation
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We propose a simple yet rich model to extend strategic games to the quantum setting, in which we define quantum Nash and correlated equilibria and study the relations between classical and quantum equilibria. Unlike all previous work that focused on qualitative questions on specific games of very small sizes, we quantitatively address the following fundamental question for general games of growing sizes: How much "advantage" can playing quantum strategies provide, if any? Two measures of the advantage are studied. 1. Since game mainly is about each player trying to maximize individual payoff, a natural measure is the increase of payoff by playing quantum strategies. We consider natural mappings between classical and quantum states, and study how well those mappings preserve equilibrium properties. Among other results, we exhibit a correlated equilibrium p whose quantum superposition counterpart [EQUATION] is far from being a quantum correlated equilibrium; actually a player can increase her payoff from almost 0 to almost 1 in a [0, 1]-normalized game. We achieve this by a tensor product construction on carefully designed base cases. The result can also be interpreted as in Meyer's comparison [47]: In a state no classical player can gain, one player using quantum computers has an huge advantage than continuing to play classically. 2. Another measure is the hardness of generating correlated equilibria, for which we propose to study correlation complexity, a new complexity measure for correlation generation. We show that there are n-bit correlated equilibria which can be generated by only one EPR pair followed by local operation (without communication), but need at least log2(n) classical shared random bits plus communication. The randomized lower bound can be improved to n, the best possible, assuming (even a much weaker version of) a recent conjecture in linear algebra. We believe that the correlation complexity, as a complexity-theoretical counterpart of the celebrated Bell's inequality, has independent interest in both physics and computational complexity theory and deserves more explorations.