IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2003.01536.html
   My bibliography  Save this paper

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

Author

Listed:
  • Dimitri J. Papageorgiou
  • Francisco Trespalacios
  • Stuart Harwood

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. ["Solving discretely-constrained Nash-Cournot games with an application to power markets." Networks and Spatial Economics 13(3), 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 this claim is false.

Suggested Citation

  • Dimitri J. Papageorgiou & Francisco Trespalacios & Stuart Harwood, 2020. "A Note on Solving Discretely-Constrained Nash-Cournot Games via Complementarity," Papers 2003.01536, arXiv.org.
    • Handle: RePEc:arx:papers:2003.01536
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2003.01536
    File Function: Latest version
    Download Restriction: no
    ---><---

    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.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Julio B. Clempner, 2021. "A Proximal/Gradient Approach for Computing the Nash Equilibrium in Controllable Markov Games," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 847-862, March.
    8. Mazidi, Peyman & Tohidi, Yaser & Ramos, Andres & Sanz-Bobi, Miguel A., 2018. "Profit-maximization generation maintenance scheduling through bi-level programming," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1045-1057.
    9. Siddiqui, Sauleh & Christensen, Adam, 2016. "Determining energy and climate market policy using multiobjective programs with equilibrium constraints," Energy, Elsevier, vol. 94(C), pages 316-325.
    10. Yanming Sun & Lin Zhang, 2019. "Full Separation or Full Integration? An Investigation of the Optimal Renewables Policy Employing Tradable Green Certificate Systems in Two Countries’ Electricity Markets," IJERPH, MDPI, vol. 16(24), pages 1-17, December.
    11. 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.
    12. Carvalho, Margarida & Pedroso, João Pedro & Telha, Claudio & Van Vyve, Mathieu, 2018. "Competitive uncapacitated lot-sizing game," International Journal of Production Economics, Elsevier, vol. 204(C), pages 148-159.
    13. Alexander Zerrahn & Daniel Huppmann, 2017. "Network Expansion to Mitigate Market Power," Networks and Spatial Economics, Springer, vol. 17(2), pages 611-644, June.
    14. Helgesen, Per Ivar & Tomasgard, Asgeir, 2018. "An equilibrium market power model for power markets and tradable green certificates, including Kirchhoff's Laws and Nash-Cournot competition," Energy Economics, Elsevier, vol. 70(C), pages 270-288.
    15. 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.
    16. Cheng Guo & Merve Bodur & Joshua A. Taylor, 2021. "Copositive Duality for Discrete Markets and Games," Papers 2101.05379, arXiv.org, revised Jan 2021.
    17. 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.
    18. Hesamzadeh, M.R. & Biggar, D.R. & Bunn, D.W. & Moiseeva, E., 2020. "The impact of generator market power on the electricity hedge market," Energy Economics, Elsevier, vol. 86(C).
    19. Carvalho, Margarida & Lodi, Andrea & Pedroso, João.P., 2022. "Computing equilibria for integer programming games," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1057-1070.
    20. Marianna De Santis & Sven de Vries & Martin Schmidt & Lukas Winkel, 2022. "A Penalty Branch-and-Bound Method for Mixed Binary Linear Complementarity Problems," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3117-3133, November.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:2003.01536. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.