  In this paper we propose a numerical method to obtain an approximation of
Nash equilibria for multi-player non-cooperative games with a special
structure. We consider the infinite horizon problem in a case which leads to a
system of Hamilton-Jacobi equations. The numerical method is based on the
Dynamic Programming Principle for every equation and on a global fixed point
iteration. We present the numerical solutions of some two-player games in one
and two dimensions. The paper has an experimental nature, but some features and
properties of the approximation scheme are discussed.
