An MPCC approach for Stochastic Stackelberg-Nash-Cournot equilibrium

In this article, we investigate a Stochastic Stackelberg-Nash-Cournot Equilibrium problem by reformulating it as a Mathematical Program with Complementarity Constraints (MPCC). The complementarity constraints are further reformulated as a system of nonsmooth equations. We characterize the followers' Nash-Cournot equilibria by studying the implicit solution of a system of equations. We outline numerical methods for the solution of a stochastic Stackelberg-Nash-Cournot Equilibrium problem with finite distribution of market demand scenarios and propose a discretization approach based on implicit numerical integration to deal with stochastic Stackelberg-Nash-Cournot Equilibrium problem with continuous distribution of demand scenarios. Finally, we discuss the two-leader Stochastic Stackelberg-Nash-Cournot Equilibrium problem.