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

Abstract

Modeling several competitive leaders and followers acting in an electricity marketleads to coupled systems of mathematical programs with equilibrium constraints,called equilibrium problems with equilibrium constraints (EPECs). We consider asimplified model for competition in electricity markets under uncertainty of demandin an electricity network as a (stochastic) multi-leader-follower game. First ordernecessary conditions are developed for the corresponding stochastic EPEC based ona result of Outrata [17]. For applying the general result an explicit representation ofthe co-derivative of the normal cone mapping to a polyhedron is derived (Proposition3.2). Later the co-derivative formula is used for verifying constraint qualificationsand for identifying M-stationary solutions of the stochastic EPEC if the demand isrepresented by a finite number of scenarios.