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
Playing large games using simple strategies
Proceedings of the 4th ACM conference on Electronic commerce
On the Complexity of Two-PlayerWin-Lose 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
Settling the Complexity of Two-Player Nash Equilibrium
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
Games of fixed rank: a hierarchy of bimatrix games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithmic Game Theory
Computational Economy Equilibrium and Application
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Performance Evaluation of a Descent Algorithm for Bi-matrix Games
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Digraphs: Theory, Algorithms and Applications
Digraphs: Theory, Algorithms and Applications
An optimization approach for approximate Nash equilibria
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
On mutual concavity and strategically-zero-sum bimatrix games
Theoretical Computer Science
On the Complexity of Approximating a Nash Equilibrium
ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
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It is shown here that the problem of computing a Nash equilibrium for two-person games can be polynomially reduced to an indefinite quadratic programming problem involving the spectrum of the adjacency matrix of a strongly connected directed graph on n vertices, where n is the total number of players' strategies. Based on that, a new method is presented for computing approximate equilibria and it is shown that its complexity is a function of the average spectral energy of the underlying graph. The implications of the strong connectedness properties on the energy and on the complexity of the method is discussed and certain classes of graphs are described for which the method is a polynomial time approximation scheme (PTAS). The worst case complexity is bounded by a subexponential function in the total number of strategies n and a comparison is made with a previously reported method with subexponential complexity.