Are weaker stationarity concepts of stochastic MPCC problems significant in absence of SMPCC-LICQ?

In this article, we study weak stationarity conditions (A- and C-) for a particular class of degenerate stochastic mathematical programming problems with complementarity constraints (SMPCC, for short). Importance of the weak stationarity concepts in absence of SMPCC-LICQ are presented through toy problems in which the point of local or global minimizers are weak stationary points rather than satisfying other stronger stationarity conditions. Finally, a well known technique to solve stochastic programming problems, namely sample average approximation (SAA) method, is studied to show the significance of the weak stationarity conditions for degenerate SMPCC problems. Consistency of weak stationary estimators are established under weaker constraint qualifications than SMPCC-LICQ.