Affiliation:
1. University of Liverpool
2. University of California at Berkeley
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 [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.
Funder
Google
National Science Foundation
Engineering and Physical Sciences Research Council
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Mathematics,Marketing,Economics and Econometrics,Statistics and Probability,Computer Science (miscellaneous)
Cited by
14 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献