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A Note on Solving Discretely-Constrained Nash-Cournot Games via Complementarity

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Listed:
  • Dimitri J. Papageorgiou

    (ExxonMobil Research and Engineering Company)

  • Francisco Trespalacios

    (ExxonMobil Research and Engineering Company)

  • Stuart Harwood

    (ExxonMobil Research and Engineering Company)

Abstract

Discretely-constrained Nash-Cournot games have attracted attention as they arise in various competitive energy production settings in which players must make one or more discrete decisions. Gabriel et al. (Netw Spat Econ 13(3):307–326 2013) claim that the set of equilibria to a discretely-constrained Nash-Cournot game coincides with the set of solutions to a corresponding discretely-constrained mixed complementarity problem. We show that one direction of this claim is false by providing counterexamples to show that there exist solutions to the discretely-constrained Nash-Cournot game that do not coincide with solutions to the discretely-constrained mixed complementarity problem. The updated theorem in this note formally states that every solution to the discretely-constrained mixed complementarity problem is a solution to the discretely-constrained Nash-Cournot game, but not vice versa.

Suggested Citation

  • Dimitri J. Papageorgiou & Francisco Trespalacios & Stuart Harwood, 2021. "A Note on Solving Discretely-Constrained Nash-Cournot Games via Complementarity," Networks and Spatial Economics, Springer, vol. 21(2), pages 325-330, June.
    • Handle: RePEc:kap:netspa:v:21:y:2021:i:2:d:10.1007_s11067-021-09524-x
    DOI: 10.1007/s11067-021-09524-x
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    References listed on IDEAS

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    1. Steven Gabriel & Sauleh Siddiqui & Antonio Conejo & Carlos Ruiz, 2013. "Solving Discretely-Constrained Nash–Cournot Games with an Application to Power Markets," Networks and Spatial Economics, Springer, vol. 13(3), pages 307-326, September.
    2. O'Neill, Richard P. & Sotkiewicz, Paul M. & Hobbs, Benjamin F. & Rothkopf, Michael H. & Stewart, William R., 2005. "Efficient market-clearing prices in markets with nonconvexities," European Journal of Operational Research, Elsevier, vol. 164(1), pages 269-285, July.
    3. Florian Leuthold & Hannes Weigt & Christian Hirschhausen, 2012. "A Large-Scale Spatial Optimization Model of the European Electricity Market," Networks and Spatial Economics, Springer, vol. 12(1), pages 75-107, March.
    4. David Fuller, J. & Çelebi, Emre, 2017. "Alternative models for markets with nonconvexities," European Journal of Operational Research, Elsevier, vol. 261(2), pages 436-449.
    5. Gabriel, Steven A. & Leuthold, Florian U., 2010. "Solving discretely-constrained MPEC problems with applications in electric power markets," Energy Economics, Elsevier, vol. 32(1), pages 3-14, January.
    6. Richard Weinhold & Steven A. Gabriel, 2020. "Discretely constrained mixed complementary problems: Application and analysis of a stylised electricity market," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(2), pages 237-249, February.
    7. Huppmann, Daniel & Siddiqui, Sauleh, 2018. "An exact solution method for binary equilibrium problems with compensation and the power market uplift problem," European Journal of Operational Research, Elsevier, vol. 266(2), pages 622-638.
    8. Cheng Guo & Merve Bodur & Joshua A. Taylor, 2021. "Copositive Duality for Discrete Markets and Games," Papers 2101.05379, arXiv.org, revised Jan 2021.
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