Annals of Operations Research

, Volume 254, Issue 1–2, pp 303–334 | Cite as

Basic theoretical foundations and insights on bilevel models and their applications to power systems

  • David PozoEmail author
  • Enzo Sauma
  • Javier Contreras
Original-Survey or Exposition


Decision making in the operation and planning of power systems is, in general, economically driven, especially in deregulated markets. To better understand the participants’ behavior in power markets, it is necessary to include concepts of microeconomics and operations research in the analysis of power systems. Particularly, game theory equilibrium models have played an important role in shaping participants’ behavior and their interactions. In recent years, bilevel games and their applications to power systems have received growing attention. Bilevel optimization models, Mathematical Program with Equilibrium Constraints and Equilibrium Problem with Equilibrium Constraints are examples of bilevel games. This paper provides an overview of the full range of formulations of non-cooperative bilevel games. Our aim is to present, in an unified manner, the theoretical foundations, classification and main techniques for solving bilevel games and their applications to power systems.


Game theory Operation research in energy Bilevel games Mathematical Program with Equilibrium Constraints Equilibrium Problem with Equilibrium Constraints 


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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Electrical EngineeringPontifical Catholic University of Rio de JaneiroRio de JaneiroBrazil
  2. 2.Pontificia Universidad Católica de ChileSantiagoChile
  3. 3.University of Castilla–La ManchaCiudad RealSpain

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