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Econ. Comput."],"published-print":{"date-parts":[[2013,5]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.1145\/2465769.2465774","type":"journal-article","created":{"date-parts":[[2013,6,5]],"date-time":"2013-06-05T12:09:34Z","timestamp":1370434174000},"page":"1-25","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":17,"title":["The Complexity of the Homotopy Method, Equilibrium Selection, and Lemke-Howson Solutions"],"prefix":"10.1145","volume":"1","author":[{"given":"Paul W.","family":"Goldberg","sequence":"first","affiliation":[{"name":"University of Liverpool"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christos H.","family":"Papadimitriou","sequence":"additional","affiliation":[{"name":"University of California at Berkeley"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rahul","family":"Savani","sequence":"additional","affiliation":[{"name":"University of Liverpool"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2013,5]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.2307\/1914231"},{"key":"e_1_2_1_2_1","first-page":"183","article-title":"On continuity of fixed points under deformations of continuous mappings","volume":"4","author":"Browder F. 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