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We present and analyze an approximation scheme for the two-dimensional game$p$-Laplacian in the framework of viscosity solutions. The approximation isbased on a semi-Lagrangian scheme which exploits the idea of $p$-averages. Westudy the properties of the scheme and prove that it converges, in particularcases, to the viscosity solution of the game $p$-Laplacian. We also present anumerical implementation of the scheme for different values of $p$; thenumerical tests show that the scheme is accurate.

A semi-Lagrangian scheme for the game $p$-Laplacian via $p$-averaging