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
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
On the Complexity of Two-PlayerWin-Lose Games
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
On the computational complexity of Nash equilibria for (0,1) bimatrix games
Information Processing Letters
The complexity of uniform Nash equilibria and related regular subgraph problems
Theoretical Computer Science
Computing exact and approximate Nash equilibria in 2-player games
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
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
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
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Parameterized two-player nash equilibrium
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
On mutual concavity and strategically-zero-sum bimatrix games
Theoretical Computer Science
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It is known that finding a Nash equilibrium for win-lose bimatrix games, i.e., two-player games where the players' payoffs are zero and one, is complete for the class PPAD. We describe a linear time algorithm which computes a Nash equilibrium for win-lose bimatrix games where the number of winning positions per strategy of each of the players is at most two. The algorithm acts on the directed graph that represents the zero-one pattern of the payoff matrices describing the game. It is based upon the efficient detection of certain subgraphs which enable us to determine the support of a Nash equilibrium.