Overdetermined problems for the normalized $p$-Laplacian

We extend the symmetry result of Serrin and Weinberger from the Laplacian operator to the highly degenerate game-theoretic $p$-Laplacian operator and show that viscosity solutions of $-{\mathrm{\Delta }}_p^{N}u=1$ in $\mathrm{\Omega }$, $u=0$ and $\frac{\mathrm{\partial }u}{\mathrm{\partial }\nu }=-c\mathrm{\ne }0$ on $\mathrm{\partial }\mathrm{\Omega }$ can only exist on a bounded domain $\mathrm{\Omega }$ if $\mathrm{\Omega }$ is a ball.