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  • Parameterized Complexity Applied in Algorithmic Game Theory

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    Parsa_2011_02Thesis.pdf (566.7Kb)
    Author(s)
    Parsa, Mahdi
    Primary Supervisor
    Estivill-Castro, Vladimir
    Other Supervisors
    Topor, Rodney
    Year published
    2011
    Metadata
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    Abstract
    The modern mathematical treatment of the study of decisions taken by participants whose interests are in conflict is now generally labeled as “game theory”. To understand these interactions the theory provides some solution concepts. An important such a concept is the notion of Nash equilibrium, which provides a way of predicting the behavior of strategic participants in situations of conflicts. However, many decision problems regarding to the computation of Nash equilibrium are computationally hard. Motivated by these hardness results, we study the parameterized complexity of the Nash equilibrium. In parameterized complexity ...
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    The modern mathematical treatment of the study of decisions taken by participants whose interests are in conflict is now generally labeled as “game theory”. To understand these interactions the theory provides some solution concepts. An important such a concept is the notion of Nash equilibrium, which provides a way of predicting the behavior of strategic participants in situations of conflicts. However, many decision problems regarding to the computation of Nash equilibrium are computationally hard. Motivated by these hardness results, we study the parameterized complexity of the Nash equilibrium. In parameterized complexity one considers computational problems in a twodimensional setting: the first dimension is the usual input size n, the second dimension is a positive integer k, the parameter. A problem is fixed-parameter tractable (FPT) if it can be solved in time f(k)nO(1) where f denotes a computable, possibly exponential, function. We show that some decision problems regarding to the computation of Nash equilibrium are hard even in parameterized complexity theory. However, we provide FPT algorithms for some other problems relevant to the computation of Nash equilibrium.
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    Thesis Type
    Thesis (PhD Doctorate)
    Degree Program
    Doctor of Philosophy (PhD)
    School
    Institute for Integrated and Intelligent Systems
    DOI
    https://doi.org/10.25904/1912/506
    Copyright Statement
    The author owns the copyright in this thesis, unless stated otherwise.
    Item Access Status
    Public
    Subject
    Game theory
    Nash equilibrium
    Fixed-parameter tractable
    Publication URI
    http://hdl.handle.net/10072/367212
    Collection
    • Theses - Higher Degree by Research

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