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Solving Discretely-Constrained Nash–Cournot Games with an Application to Power Markets

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  • Steven Gabriel
  • Sauleh Siddiqui
  • Antonio Conejo
  • Carlos Ruiz

Abstract

This paper provides a methodology to solve Nash–Cournot energy production games allowing some variables to be discrete. Normally, these games can be stated as mixed complementarity problems but only permit continuous variables in order to make use of each producer’s Karush–Kuhn–Tucker conditions. The proposed approach allows for more realistic modeling and a compromise between integrality and complementarity to avoid infeasible situations. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • 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.
    • Handle: RePEc:kap:netspa:v:13:y:2013:i:3:p:307-326
    DOI: 10.1007/s11067-012-9182-2
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    References listed on IDEAS

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    1. Steven A. Gabriel & Antonio J. Conejo & J. David Fuller & Benjamin F. Hobbs & Carlos Ruiz, 2013. "Complementarity Modeling in Energy Markets," International Series in Operations Research and Management Science, Springer, edition 127, number 978-1-4419-6123-5, December.
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    7. 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.
    8. Jonathan F. Bard, 1983. "An Efficient Point Algorithm for a Linear Two-Stage Optimization Problem," Operations Research, INFORMS, vol. 31(4), pages 670-684, August.
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    12. S A Gabriel & Y Shim & A J Conejo & S de la Torre & R García-Bertrand, 2010. "A Benders decomposition method for discretely-constrained mathematical programs with equilibrium constraints," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(9), pages 1404-1419, September.
    13. SMEERS, Yves, 2003. "Market incompleteness in regional electricity transmission. Part II: the forward and real time markets," LIDAM Reprints CORE 1633, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. 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.
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    Cited by:

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    2. Dimitri J. Papageorgiou & Francisco Trespalacios & Stuart Harwood, 2020. "A Note on Solving Discretely-Constrained Nash-Cournot Games via Complementarity," Papers 2003.01536, arXiv.org.
    3. Cheng Guo & Merve Bodur & Joshua A. Taylor, 2021. "Copositive Duality for Discrete Markets and Games," Papers 2101.05379, arXiv.org, revised Jan 2021.
    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. Gabriele Dragotto & Rosario Scatamacchia, 2023. "The Zero Regrets Algorithm: Optimizing over Pure Nash Equilibria via Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1143-1160, September.
    6. 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.
    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. Zerrahn, Alexander & Huppmann, Daniel, 2014. "Network Expansion to Mitigate Market Power: How Increased Integration Fosters Welfare," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100459, Verein für Socialpolitik / German Economic Association.
    9. 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).
    10. 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.
    11. Alexander Zerrahn & Daniel Huppmann, 2017. "Network Expansion to Mitigate Market Power," Networks and Spatial Economics, Springer, vol. 17(2), pages 611-644, June.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. Acuña, Luceny Guzmán & Ríos, Diana Ramírez & Arboleda, Carlos Paternina & Ponzón, Esneyder González, 2018. "Cooperation model in the electricity energy market using bi-level optimization and Shapley value," Operations Research Perspectives, Elsevier, vol. 5(C), pages 161-168.

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