Pure characteristics demand models and distributionally robust mathematical programs with stochastic complementarity constraints

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 DRMP-SCC is monotone linear (LCP). To deal ambiguity involved variables in LCP, we use approach. Moreover, propose an approximation regularization discretization to solve DRMP-SCC, which two-stage nonconvex-nonconcave minimax optimization problem. prove convergence regarding optimal solution sets, values stationary points parameter goes zero sample size infinity. Finally, preliminary numerical results for investigating distributional robustness are reported illustrate effectiveness efficiency our approaches.