  We formulate pure characteristics demand models under uncertainties of
probability distributions as distributionally robust mathematical programs with
stochastic complementarity constraints (DRMP-SCC). For any fixed first-stage
variable and a random realization, the second-stage problem of DRMP-SCC is a
monotone linear complementarity problem (LCP). To deal with uncertainties of
probability distributions of the involved random variables in the stochastic
LCP, we use the distributionally robust approach. Moreover, we propose an
approximation problem with regularization and discretization to solve DRMP-SCC,
which is a two-stage nonconvex-nonconcave minimax optimization problem. We
prove the convergence of the approximation problem to DRMP-SCC regarding the
optimal solution sets, optimal values and stationary points as the
regularization parameter goes to zero and the sample size goes to infinity.
Finally, preliminary numerical results for investigating distributional
robustness of pure characteristics demand models are reported to illustrate the
effectiveness and efficiency of our approaches.
