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dc.contributor.authorEstivill-Castro, Vladimiren_US
dc.contributor.authorParsa, Mahdien_US
dc.contributor.editorRod Downey and Prabhu Manyemen_US
dc.description.abstractIn this paper we show that some decision problems regarding the computation of Nash equilibria are to be considered particularly hard. Most decision problems regarding Nash equilibria have been shown to be NP-complete. While some NP-complete problems can find an alternative to tractability with the tools of Parameterized Complexity Theory, it is also the case that some classes of problems do not seem to have fixed-parameter tractable algorithms. We show that k-Uniform Nash and k-Minimal Nash support are W[2]-hard. Given a game G=(A,B) and a nonnegative integer k, the k-Uniform Nash problem asks whether G has a uniform Nash equilibrium of size k. The k-Minimal Nash support asks whether has Nash equilibrium such that the support of eacGh player's Nash strategy has size equal to or less than k. First, we show that k-Uniform Nash (with k as the parameter) is W[2]-hard even when we have 2 players, or fewer than 4 different integer values in the matrices. Second, we illustrate that even in zerosum games k-Minimal Nash support is W[2]-hard (a sample Nash equilibrium in a zero-sum 2-player game can be found in polynomial time (von Stengel 2002)). Thus, it must be the case that other more general decision problems are also W[2]-hard. Therefore, the possible parameters for fixed parameter tractability in those decision problems regarding Nash equilibria seem elusive.en_US
dc.publisherAustralian Computer Societyen_US
dc.publisher.placeSydney, Australiaen_US
dc.relation.ispartofconferencenameCATS 2009 (Computing: The Australasian Theory Symposium)en_US
dc.relation.ispartofconferencetitleProceedings of the 15th Computing: The Australasian Theory Symposium (CATS 2009)en_US
dc.relation.ispartoflocationWellington, New Zealanden_US
dc.subject.fieldofresearchAnalysis of Algorithms and Complexityen_US
dc.titleComputing Nash equilibria gets harder - new results show hardness even for Parameterized Complexityen_US
dc.typeConference outputen_US
dc.type.descriptionE1 - Conference Publications (HERDC)en_US
dc.type.codeE - Conference Publicationsen_US
gro.facultyGriffith Sciences, School of Information and Communication Technologyen_US
gro.hasfulltextNo Full Text

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