Exploiting Concavity in Bimatrix Games: New Polynomially Tractable Subclasses

  title={Exploiting Concavity in Bimatrix Games: New Polynomially Tractable Subclasses},
  author={Spyros C. Kontogiannis and Paul G. Spirakis},
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… 

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