WIAS Preprint No. 1433, (2009)

Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market



Authors

  • Henrion, René
  • Outrata, Jiří
  • Surowiec, Thomas
    ORCID: 0000-0003-2473-4984

2010 Mathematics Subject Classification

  • 90C30 49J53

Keywords

  • Equilibrium problems with equilibrium constraints, EPEC, $M$-stationary solutions, electricity spot market, calmness

Abstract

We consider an equilibrium problem with equilibrium constraints (EPEC) as it arises from modeling competition in an electricity spot market (under ISO regulation). For a characterization of equilibrium solutions, so-called $M$-stationarity conditions are derived. This requires a structural analysis of the problem first (constraint qualifications, strong regularity). Second, the calmness property of a certain multifunction has to be verified in order to justify $M$-stationarity. Third, for stating the stationarity conditions, the co-derivative of a normal cone mapping has to be calculated. Finally, the obtained necessary conditions are made fully explicit in terms of the problem data for one typical constellation. A simple two-settlements example serves as an illustration.

Appeared in

  • ESAIM Control Optim. Calc. Var., 18 (2012) pp. 295--317.

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