A stochastic differential game for the inhomogeneous $infty$-Laplace equation

Given a bounded $mathcaligr{C}^2$ domain $Gsubset{mathbb{R}}^m$, functions $ginmathcaligr{C}(partial G,{mathbb{R}})$ and $hinmathcaligr {C}(bar{G},{mathbb{R}}setminus{0})$, let $u$ denote the unique viscosity solution to the equation $-2Delta_{infty}u=h$ in $G$ with boundary data $g$. We provide a representation for $u$ as the value of a two-player zero-sum stochastic differential game.