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.
A two-player stochastic differential game representation has recently been obtained for solutions of the equation -Delta_infty u=h in a calC^2 domain with Dirichlet boundary condition, where h is continuous and takes values in RRsetminus{0}. Under ap
propriate assumptions, including smoothness of u, the vanishing delta limit law of the state process, when both players play delta-optimally, is identified as a diffusion process with coefficients given explicitly in terms of derivatives of the function u.
