IDEAS home Printed from https://ideas.repec.org/a/kap/netspa/v21y2021i2d10.1007_s11067-021-09524-x.html
   My bibliography  Save this article

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

Author

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11067-021-09524-x
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11067-021-09524-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hassan Shavandi & Mehrdad Pirnia & J. David Fuller, 2018. "Extended opportunity cost model to find near equilibrium electricity prices under non-convexities," Papers 1809.09734, arXiv.org.
    2. Shavandi, Hassan & Pirnia, Mehrdad & Fuller, J. David, 2019. "Extended opportunity cost model to find near equilibrium electricity prices under non-convexities," Applied Energy, Elsevier, vol. 240(C), pages 251-264.
    3. Vadim Borokhov, 2022. "Utilizing the redundant constraints for the uplift payment elimination," Operational Research, Springer, vol. 22(2), pages 1377-1402, April.
    4. Hesamzadeh, M. & Holmberg, P. & Sarfati, M., 2018. "Simulation and Evaluation of Zonal Electricity Market Designs," Cambridge Working Papers in Economics 1829, Faculty of Economics, University of Cambridge.
    5. Alexander Zerrahn & Daniel Huppmann, 2017. "Network Expansion to Mitigate Market Power," Networks and Spatial Economics, Springer, vol. 17(2), pages 611-644, June.
    6. Huppmann, Daniel & Egerer, Jonas, 2015. "National-strategic investment in European power transmission capacity," European Journal of Operational Research, Elsevier, vol. 247(1), pages 191-203.
    7. Alexander Zerrahn & Daniel Huppmann, 2014. "Network Expansion to Mitigate Market Power: How Increased Integration Fosters Welfare," Discussion Papers of DIW Berlin 1380, DIW Berlin, German Institute for Economic Research.
    8. 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.
    9. Dávid Csercsik & László Á. Kóczy, 2017. "Efficiency and Stability in Electrical Power Transmission Networks: a Partition Function Form Approach," Networks and Spatial Economics, Springer, vol. 17(4), pages 1161-1184, December.
    10. Diana Bottger & Philipp Hartel, 2021. "On Wholesale Electricity Prices and Market Values in a Carbon-Neutral Energy System," Papers 2105.01127, arXiv.org.
    11. Dávid Csercsik, 2016. "Competition and Cooperation in a Bidding Model of Electrical Energy Trade," Networks and Spatial Economics, Springer, vol. 16(4), pages 1043-1073, December.
    12. Paul Neetzow & Roman Mendelevitch & Sauleh Siddiqui, 2018. "Modeling Coordination between Renewables and Grid: Policies to Mitigate Distribution Grid Constraints Using Residential PV-Battery Systems," Discussion Papers of DIW Berlin 1766, DIW Berlin, German Institute for Economic Research.
    13. Olufolajimi Oke & Daniel Huppmann & Max Marshall & Ricky Poulton & Sauleh Siddiqui, 2019. "Multimodal Transportation Flows in Energy Networks with an Application to Crude Oil Markets," Networks and Spatial Economics, Springer, vol. 19(2), pages 521-555, June.
    14. Villalobos, Cristian & Negrete-Pincetic, Matías & Figueroa, Nicolás & Lorca, Álvaro & Olivares, Daniel, 2021. "The impact of short-term pricing on flexible generation investments in electricity markets," Energy Economics, Elsevier, vol. 98(C).
    15. Löschenbrand, Markus, 2020. "Finding multiple Nash equilibria via machine learning-supported Gröbner bases," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1178-1189.
    16. Jonas Egerer, 2016. "Open Source Electricity Model for Germany (ELMOD-DE)," Data Documentation 83, DIW Berlin, German Institute for Economic Research.
    17. Härtel, Philipp & Korpås, Magnus, 2021. "Demystifying market clearing and price setting effects in low-carbon energy systems," Energy Economics, Elsevier, vol. 93(C).
    18. Clemens Gerbaulet & Alexander Weber, 2014. "Is There Still a Case for Merchant Interconnectors?: Insights from an Analysis of Welfare and Distributional Aspects of Options for Network Expansion in the Baltic Sea Region," Discussion Papers of DIW Berlin 1404, DIW Berlin, German Institute for Economic Research.
    19. 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.
    20. Böttger, Diana & Härtel, Philipp, 2022. "On wholesale electricity prices and market values in a carbon-neutral energy system," Energy Economics, Elsevier, vol. 106(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:netspa:v:21:y:2021:i:2:d:10.1007_s11067-021-09524-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.