Parameterized Complexity Applied in Algorithmic Game Theory

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Author(s)
Primary Supervisor
Estivill-Castro, Vladimir
Other Supervisors
Topor, Rodney
Year published
2011
Metadata
Show full item recordAbstract
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 ...
View more >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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View more >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
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