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Equilibrium Problems with Equilibrium Constraints

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Complementarity Modeling in Energy Markets

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 180))

Abstract

The previous chapter presented mathematical programs for solving leaderfollower (Stackelberg) games when a single leader correctly anticipates the equilibrium reaction of followers, who in turn naively believe that the leader’s decisions are exogenous and fixed. This chapter introduces a type of mathematical program that is useful for modeling such games when there is more than one leader, and one wants to find an equilibrium among them: Equilibrium Problems with Equilibrium Constraints (EPECs). First, we present a general EPEC formulation (Section 7.2) and the basic diagonalization approach to solving EPECs, including a simple example. We then summarize some of their many applications to energy markets (Section 7.3), including the three examples of energy market EPECs that we feature in this chapter.

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Author information

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Maryland, College Park, MD, USA

    Steven A. Gabriel

  2. University of Castilla – La Mancha, Campus Universitario s/n, Ciudad Real, Spain

    Antonio J. Conejo

  3. Department of Management Sciences, University of Waterloo, Waterloo, Ontario, Canada

    J. David Fuller

  4. Department of Geography and Environmental Engineering, The Johns Hopkins University, Baltimore, MD, USA

    Benjamin F. Hobbs

  5. European Foundation for New Energy – EDF École Centrale Paris and Supélec, Châtenay-Malabry, France

    Carlos Ruiz (Chair on Systems Science and the Energetic Challenge)

Authors
  1. Steven A. Gabriel
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  2. Antonio J. Conejo
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  3. J. David Fuller
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  4. Benjamin F. Hobbs
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  5. Carlos Ruiz
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Gabriel, S.A., Conejo, A.J., Fuller, J.D., Hobbs, B.F., Ruiz, C. (2013). Equilibrium Problems with Equilibrium Constraints. In: Complementarity Modeling in Energy Markets. International Series in Operations Research & Management Science, vol 180. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6123-5_7

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