We present and analyze a numerical approximation of the two-dimensional Dirichlet problem for the game p-Laplacian based on a semi-Lagrangian scheme. We start from recalling the definition of game p-Laplacian, which has been recently introduced by Peres and Sheffield to model the continuous limit value of certain stochastic games (tug-of-war with noise). In the homogeneous case (no right-hand side), variational and game p-Laplacian operators are essentially the same, but in the general case the variational structure of the problem is no more available. The key tool for our approximation scheme is then the discretization of the p-operators in terms of p-averages of a finite number of values. We study the property of the scheme and prove that it converges, under certain hypotheses, to the viscosity solution of the game p-Laplacian problem. Then we present a number of numerical tests to show that the scheme is accurate. (Joint work with M. Falcone, T. Giorgi and R.G. Smits)