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arXiv · 1006.5352

The Complexity of the Homotopy Method, Equilibrium Selection, and Lemke-Howson Solutions

Paul W. Goldberg·Christos H. Papadimitriou·Rahul Savani
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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.

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Paul W. Goldberg, Christos H. Papadimitriou, Rahul Savani. 2010-06-28. The Complexity of the Homotopy Method, Equilibrium Selection, and Lemke-Howson Solutions. https://arxiv.org/abs/1006.5352

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