On $M$-stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling

summary:Modeling several competitive leaders and followers acting in an electricity market leads to coupled systems of mathematical programs with equilibrium constraints, called equilibrium problems with equilibrium constraints (EPECs). We consider a simplified model for competition in electricity markets under uncertainty of demand in an electricity network as a (stochastic) multi-leader-follower game. First order necessary conditions are developed for the corresponding stochastic EPEC based on a result of Outrata. For applying the general result an explicit representation of the co-derivative of the normal cone mapping to a polyhedron is derived. Then the co-derivative formula is used for verifying constraint qualifications and for identifying $M$-stationary solutions of the stochastic EPEC if the demand is represented by a finite number of scenarios