Geodesic
On $M$-stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling
Applications of Mathematics, Tome 52 (2007) no. 6, pp. 473-494.

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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.
DOI : 10.1007/s10492-007-0028-z
Classification : 90C15, 91B26, 91B52
Keywords: electricity markets; bidding; noncooperative games; equilibrium constraint; EPEC; optimality condition; co-derivative; random demand 
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     title = {On $M$-stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling},
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Henrion, René; Römisch, Werner. On $M$-stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling. Applications of Mathematics, Tome 52 (2007) no. 6, pp. 473-494. doi : 10.1007/s10492-007-0028-z. http://geodesic.mathdoc.fr/articles/10.1007/s10492-007-0028-z/

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