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### Paper:

TR06-081 | 19th May 2006 00:00

#### Polynomial Algorithms for Approximating Nash Equilibria of Bimatrix Games

TR06-081
Authors: Spyros Kontogiannis, Panagiota Panagopoulou, Paul Spirakis
Publication: 25th June 2006 20:01
Keywords:

Abstract:

We focus on the problem of computing an $\epsilon$-Nash equilibrium of a bimatrix game, when $\epsilon$ is an absolute constant.
We present a simple algorithm for computing a $\frac{3}{4}$-Nash equilibrium for any bimatrix game in strongly polynomial time and
we next show how to extend this algorithm so as to obtain a (potentially stronger) parameterized approximation.
Namely, we present an algorithm that computes a $\frac{2+\lambda+\epsilon}{4}$-Nash equilibrium for any $\epsilon$, where $\lambda$
is the minimum, among all Nash equilibria, expected payoff of either player. The suggested algorithm runs in time polynomial in $\frac{1}{\epsilon}$ and the number of strategies available to the players.

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