dc.contributor.author | Daskalakis, Constantinos | |
dc.date.accessioned | 2012-09-21T15:26:15Z | |
dc.date.available | 2012-09-21T15:26:15Z | |
dc.date.issued | 2011 | |
dc.identifier.issn | 1071-9040 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/73096 | |
dc.description.abstract | We show that computing a relative---that is, multiplicative as opposed to additive---approximate Nash equilibrium in two-player games is PPAD-complete, even for constant values of the approximation. Our result is the first constant inapproximability result for the problem, since the appearance of the original results on the complexity of the Nash equilibrium [8, 5, 7]. Moreover, it provides an apparent---assuming that PPAD ⊈ TIME(n[superscript O(log n)])---dichotomy between the complexities of additive and relative notions of approximation, since for constant values of additive approximation a quasi-polynomial-time algorithm is known [22]. Such a dichotomy does not arise for values of the approximation that scale with the size of the game, as both relative and additive approximations are PPAD-complete [7]. As a byproduct, our proof shows that the Lipton-Markakis-Mehta sampling lemma is not applicable to relative notions of constant approximation, answering in the negative direction a question posed to us by Shang-Hua Teng [26]. | en_US |
dc.description.sponsorship | Alfred P. Sloan Foundation (Fellowship) | en_US |
dc.description.sponsorship | National Science Foundation (U.S.) (CAREER Award CCF-095396) | en_US |
dc.language.iso | en_US | |
dc.publisher | Society for Industrial and Applied Mathematics | en_US |
dc.relation.isversionof | http://dl.acm.org/citation.cfm?id=2133036.2133153&coll=DL&dl=ACM&CFID=117975919&CFTOKEN=69611958 | en_US |
dc.rights | Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. | en_US |
dc.source | SIAM | en_US |
dc.title | On the complexity of approximating a nash equilibrium | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Constantinos Daskalakis. 2011. On the complexity of approximating a Nash equilibrium. In Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '11). SIAM 1498-1517. SIAM ©2011 | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory | en_US |
dc.contributor.mitauthor | Daskalakis, Constantinos | |
dc.relation.journal | Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '11) | en_US |
dc.eprint.version | Final published version | en_US |
dc.type.uri | http://purl.org/eprint/type/ConferencePaper | en_US |
dc.identifier.orcid | https://orcid.org/0000-0002-5451-0490 | |
mit.license | PUBLISHER_POLICY | en_US |
mit.metadata.status | Complete | |