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In this paper we first investigate zero-sum two-player stochasticdifferential games with reflection with the help of theory of ReflectedBackward Stochastic Differential Equations (RBSDEs). We will establish thedynamic programming principle for the upper and the lower value functions ofthis kind of stochastic differential games with reflection in astraight-forward way. Then the upper and the lower value functions are provedto be the unique viscosity solutions of the associated upper and the lowerHamilton-Jacobi-Bellman-Isaacs equations with obstacles, respectively. Themethod differs heavily from those used for control problems with reflection, ithas its own techniques and its own interest. On the other hand, we also prove anew estimate for RBSDEs being sharper than that in El Karoui, Kapoudjian,Pardoux, Peng and Quenez [7], which turns out to be very useful because itallows to estimate the $L^p$-distance of the solutions of two different RBSDEsby the $p$-th power of the distance of the initial values of the drivingforward equations. We also show that the unique viscosity solution of theapproximating Isaacs equation which is constructed by the penalization methodconverges to the viscosity solution of the Isaacs equation with obstacle.

Stochastic differential games with reflection and related obstacle problems for Isaacs equations