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  • Single parameter FPT-algorithms for non-trivial games

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    64433_1.pdf (271.7Kb)
    Author(s)
    Estivill-Castro, Vladimir
    Parsa, Mahdi
    Griffith University Author(s)
    Estivill-Castro, Vladimir
    Parsa, Mahdi
    Year published
    2011
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    Abstract
    We know that k-Uniform Nash is W[2]-Complete when we consider imitation symmetric win-lose games (with k as the parameter) even when we have two players. However, this paper provides positive results regarding Nash equilibria. We show that consideration of sparse games or limitations of the support result in fixed-parameter algorithms with respect to one parameter only for the k-Uniform Nash problem. That is, we show that a sample uniform Nash equilibrium in r-sparse imitation symmetric win-lose games is not as hard because it can be found in FPT time (i.e polynomial in the size of the game, but maybe exponential ...
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    We know that k-Uniform Nash is W[2]-Complete when we consider imitation symmetric win-lose games (with k as the parameter) even when we have two players. However, this paper provides positive results regarding Nash equilibria. We show that consideration of sparse games or limitations of the support result in fixed-parameter algorithms with respect to one parameter only for the k-Uniform Nash problem. That is, we show that a sample uniform Nash equilibrium in r-sparse imitation symmetric win-lose games is not as hard because it can be found in FPT time (i.e polynomial in the size of the game, but maybe exponential in r). Moreover, we show that, although NP-Complete, the problem of Best Nash Equilibrium is also x-parameter tractable.
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    Journal Title
    Lecture Notes in Computer science
    Volume
    6460
    DOI
    https://doi.org/10.1007/978-3-642-19222-7_13
    Copyright Statement
    © 2011 Springer Berlin / Heidelberg. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. The original publication is available at www.springerlink.com
    Subject
    Analysis of Algorithms and Complexity
    Publication URI
    http://hdl.handle.net/10072/39590
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    • Journal articles

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