  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
\RR\setminus\{0\}. Under appropriate 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.
