Mathematical Programming: Series A and B
The ultimate planar convex hull algorithm
SIAM Journal on Computing
A probabilistic analysis of the simplex method
A probabilistic analysis of the simplex method
On the average number of maxima in a set of vectors
Information Processing Letters
On total functions, existence theorems and computational complexity
Theoretical Computer Science
On the convex hull of uniform random points in a simple dpolytope
Discrete & Computational Geometry
Convex hulls of samples from spherically symmetric distributions
Discrete Applied Mathematics
A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
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
Discrete aspects of stochastic geometry
Handbook of discrete and computational geometry
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Playing large games using simple strategies
Proceedings of the 4th ACM conference on Electronic commerce
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Journal of the ACM (JACM)
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Exponentially Many Steps for Finding a Nash Equilibrium in a Bimatrix Game
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Computing correlated equilibria in multi-player games
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Computing equilibria in multi-player games
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Complexity results about Nash equilibria
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Games of fixed rank: a hierarchy of bimatrix games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate Equilibria for Strategic Two Person Games
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Strategic Characterization of the Index of an Equilibrium
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Settling the complexity of computing two-player Nash equilibria
Journal of the ACM (JACM)
Polynomial algorithms for approximating Nash equilibria of bimatrix games
Theoretical Computer Science
Random bimatrix games are asymptotically easy to solve (a simple proof)
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
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
Well supported approximate equilibria in bimatrix games: a graph theoretic approach
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Efficient algorithms for constant well supported approximate equilibria in bimatrix games
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Random Bimatrix Games Are Asymptotically Easy to Solve (A Simple Proof)
Theory of Computing Systems
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We consider Nash equilibria in 2-player random games and analyze a simple Las Vegas algorithm for finding an equilibrium. The algorithm is combinatorial and always finds a Nash equilibrium; on m x n payoff matrices,it runs in time O(a^2 n\log \log n + n^2 m\log \log n) with high probability. Our main tool is a polytope formulation of equilibria.