The Complexity of the Homotopy Method, Equilibrium Selection, and Lemke-Howson Solutions
Abstract
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]. These results show that our techniques can be widely applied and suggest that the PSPACE-completeness of implementing homotopy methods is a general principle.
Cite
@article{arxiv.1006.5352,
title = {The Complexity of the Homotopy Method, Equilibrium Selection, and Lemke-Howson Solutions},
author = {Paul W. Goldberg and Christos H. Papadimitriou and Rahul Savani},
journal= {arXiv preprint arXiv:1006.5352},
year = {2011}
}
Comments
23 pages, 1 figure; to appear in FOCS 2011 conference