WIAS Preprint No. 1433, (2009)

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


  • Henrion, René
    ORCID: 0000-0001-5572-7213
  • Outrata, Jiří
  • Surowiec, Thomas
    ORCID: 0000-0003-2473-4984

2010 Mathematics Subject Classification

  • 90C30 49J53


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




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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