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Supply Function Equilibrium in a Constrained Transmission System

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  • Robert Wilson

Abstract

This article characterizes a supply function equilibrium in an auction market constrained by limited capacities of links in a transportation network and limited input/output capacities of participants. The formulation is adapted to a wholesale spot market for electricity managed by the operator of the transmission system. The results are derived using the calculus of variations to obtain the Euler conditions and the transversality conditions that characterize a Nash equilibrium in an auction in which bids are as supply functions, and quantities and payments are based either on nodal prices or pay-as-bid.
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Suggested Citation

  • Robert Wilson, 2005. "Supply Function Equilibrium in a Constrained Transmission System," Levine's Bibliography 784828000000000087, UCLA Department of Economics.
    • Handle: RePEc:cla:levrem:784828000000000087
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    File URL: http://faculty-gsb.stanford.edu/wilson/Personal%20pdf/WilsonSFE.pdf
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    References listed on IDEAS

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    2. Alexander Teytelboym & Shengwu Li & Scott Duke Kominers & Mohammad Akbarpour & Piotr Dworczak, 2021. "Discovering Auctions: Contributions of Paul Milgrom and Robert Wilson," Scandinavian Journal of Economics, Wiley Blackwell, vol. 123(3), pages 709-750, July.
    3. Holmberg, Pär & Philpott, Andrew, 2012. "Supply Function Equilibria in Networks with Transport Constraints," Working Paper Series 945, Research Institute of Industrial Economics, revised 10 Aug 2015.
    4. Benjamin Heymann & Alejandro Jofré, 2024. "Procurement auctions with losses," Computational Management Science, Springer, vol. 21(2), pages 1-20, December.
    5. Holmberg, Pär & Lazarczyk, Ewa, 2012. "Congestion Management in Electricity Networks: Nodal, Zonal and Discriminatory Pricing," Working Paper Series 915, Research Institute of Industrial Economics.
    6. Holmberg, Pär & Willems, Bert, 2015. "Relaxing competition through speculation: Committing to a negative supply slope," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 236-266.
    7. Pär Holmberg & Keith Ruddell & Bert Willems, 2025. "Multi-Product Supply Function Equilibria," Working Papers hal-05294356, HAL.
    8. Majid Al-Gwaiz & Xiuli Chao & Owen Q. Wu, 2017. "Understanding How Generation Flexibility and Renewable Energy Affect Power Market Competition," Manufacturing & Service Operations Management, INFORMS, vol. 19(1), pages 114-131, February.
    9. Nicholas Ryan, 2017. "The Competitive Effects of Transmission Infrastructure in the Indian Electricity Market," NBER Working Papers 23106, National Bureau of Economic Research, Inc.
    10. Hamid Nazerzadeh & Georgia Perakis, 2016. "Technical Note—Nonlinear Pricing Competition with Private Capacity Information," Operations Research, INFORMS, vol. 64(2), pages 329-340, April.
    11. Hunt Allcott, 2012. "The Smart Grid, Entry, and Imperfect Competition in Electricity Markets," NBER Working Papers 18071, National Bureau of Economic Research, Inc.
    12. Holmberg, Pär & Newbery, David & Ralph, Daniel, 2013. "Supply function equilibria: Step functions and continuous representations," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1509-1551.
    13. Matteo Bizzarri, 2026. "Multilateral Market Power in Input-Output Networks," Papers 2603.21932, arXiv.org.
    14. Robert B. Wilson, 2021. "Strategic Analysis of Auctions," Econometrica, Econometric Society, vol. 89(2), pages 555-561, March.
    15. Péter Biró & Gyula Magyarkuti, 2021. "The Work of Milgrom and Wilson in the Theory and Practical Application of Auctions," Financial and Economic Review, Magyar Nemzeti Bank (Central Bank of Hungary), vol. 20(1), pages 127-151.
    16. Justus Haucap, 2020. "Nobelpreis für Robert Wilson und Paul Milgrom: Zwei Ökonomen, die echte Märkte schufen [Nobel Prize for Robert Wilson and Paul Milgrom: Two Economists who Created Real Markets]," Wirtschaftsdienst, Springer;ZBW - Leibniz Information Centre for Economics, vol. 100(12), pages 969-975, December.
    17. Nobel Prize Committee, 2020. "Improvements to auction theory and inventions of new auction formats," Nobel Prize in Economics documents 2020-2, Nobel Prize Committee.
    18. Pär Holmberg & Andy Philpott, 2014. "Supply function equilibria in transportation networks," Working Papers EPRG 1401, Energy Policy Research Group, Cambridge Judge Business School, University of Cambridge.
    19. Mohammad Rasouli & Demosthenis Teneketzis, 2021. "Economizing the Uneconomic: Markets for Reliable, Sustainable, and Price Efficient Electricity," Sustainability, MDPI, vol. 13(8), pages 1-38, April.
    20. Pär Holmberg, 2009. "Supply function equilibria of pay-as-bid auctions," Journal of Regulatory Economics, Springer, vol. 36(2), pages 154-177, October.
    21. Holmberg, P. & Philpott, A.B., 2018. "On supply-function equilibria in radial transmission networks," European Journal of Operational Research, Elsevier, vol. 271(3), pages 985-1000.
    22. Holmberg, Pär & Newbery, David, 2010. "The supply function equilibrium and its policy implications for wholesale electricity auctions," Utilities Policy, Elsevier, vol. 18(4), pages 209-226, December.
    23. Matteo Bizzarri, 2025. "General equilibrium with competition in schedules and input-output networks: an existence result," CSEF Working Papers 765, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    24. Wittwer, Milena, 2020. "Interconnected pay-as-bid auctions," Games and Economic Behavior, Elsevier, vol. 121(C), pages 506-530.

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