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
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Node-and edge-deletion NP-complete problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
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
Complexity results about Nash equilibria
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
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
Fast exponential algorithms for maximum γ-regular induced subgraph problems
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
New results on the complexity of uniformly mixed nash equilibria
WINE'05 Proceedings of the First international conference on Internet and Network Economics
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
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We investigate the complexity of finding uniformly mixed Nash equilibria (that is, equilibria in which all played strategies are played with the same probability). We show that, even in very simple win/lose bimatrix games, deciding the existence of uniformly mixed equilibria in which the support of one (or both) of the players is at most or at least a given size is an NP-complete problem. Motivated by these results, we also give NP-completeness results for problems related to finding a regular induced subgraph of a certain size or regularity in a given graph, which can be of independent interest.