# Exploiting Concavity in Bimatrix Games: New Polynomially Tractable Subclasses

@inproceedings{Kontogiannis2010ExploitingCI, title={Exploiting Concavity in Bimatrix Games: New Polynomially Tractable Subclasses}, author={Spyros C. Kontogiannis and Paul G. Spirakis}, booktitle={APPROX-RANDOM}, year={2010} }

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…

## 5 Citations

### Approximability of Symmetric Bimatrix Games and Related Experiments

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This work presents a simple quadratic formulation for the problem of computing Nash equilibria in symmetric bimatrix games, inspired by the well-known formulation of Mangasarian and Stone, and proves that any KKT point of this formulation is also a stationary point, and vice versa.

### Rank-1 bimatrix games: a homeomorphism and a polynomial time algorithm

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The approach provably extends the class of dueling games for which equilibria can be computed, and introduces a new dueling game, the matching duel, on which prior methods fail to be computationally feasible but upon which the authors' reduction can be applied.

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