Exponential lower bounds for finding Brouwer fixed points
Journal of Complexity
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
Settling the complexity of computing two-player Nash equilibria
Journal of the ACM (JACM)
On the complexity of 2D discrete fixed point problem
Theoretical Computer Science
The Complexity of Computing a Nash Equilibrium
SIAM Journal on Computing
On the Complexity of Nash Equilibria and Other Fixed Points
SIAM Journal on Computing
Graphical models for game theory
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
Hi-index | 0.00 |
We show that the widely used homotopy method for solving fixpoint problems, as well as the Harsanyi-Selten equilibrium selection process for games, are PSPACE-complete to implement. Extending our result for the Harsanyi-Selten process, we show that several other homotopy-based algorithms for finding equilibria of games are also PSPACE-complete to implement. A further application of our techniques yields the result that it is PSPACE-complete to compute any of the equilibria that could be found via the classical Lemke-Howson algorithm, a complexity-theoretic strengthening of the result in Savani and von Stengel [2006]. These results show that our techniques can be widely applied and suggest that the PSPACE-completeness of implementing homotopy methods is a general principle.