We focus on studying stochastic nonlinear complementarity problems
(SNCP) and stochastic mathematical programs with equilibrium
constraints (SMPEC). Instead of the NCP functions employed in the literature, we use the restricted
NCP functions to define expected residual minimization formulations
for SNCP and SMPEC. We then discuss level set conditions and error
bounds of the new formulation. Numerical examples show that the new
formulations have some desirable properties which the existing ones
do not have.