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.