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APPROX
2010
Springer

Exploiting Concavity in Bimatrix Games: New Polynomially Tractable Subclasses

8 years 7 months ago
Exploiting Concavity in Bimatrix Games: New Polynomially Tractable Subclasses
Abstract. We study the fundamental problem of computing an arbitrary Nash equilibrium in bimatrix games. We start by proposing a novel characterization of the set of Nash equilibria, via a bijective map to the solution set of a (parameterized) quadratic program, whose feasible space is the (highly structured) set of correlated equilibria. We then proceed by proposing new subclasses of bimatrix games for which either an exact polynomial-time construction, or at least a FPTAS, is possible. In particular, we introduce the notion of mutual (quasi-) concavity of a bimatrix game, which assures (quasi-) convexity of our quadratic program, for at least one value of the parameter. For mutually concave bimatrix games, we provide a polynomial-time computation of a Nash equilibrium, based on the polynomial tractability of convex quadratic programming. For the mutually quasi-concave games, we provide (to our knowledge) the first FPTAS for the construction of a Nash equilibrium. Of course, for these...
Spyros C. Kontogiannis, Paul G. Spirakis
Added 26 Oct 2010
Updated 26 Oct 2010
Type Conference
Year 2010
Where APPROX
Authors Spyros C. Kontogiannis, Paul G. Spirakis
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