IDEAS home Printed from https://ideas.repec.org/p/enp/wpaper/eprg0829.html
   My bibliography  Save this paper

Supply Function Equilibria: Step functions and continuous representations

Author

Listed:
  • Pär Holmberg

    (Research Institute of Industrial Economics, Stockholm)

  • David Newbery

    (Faculty of Economics, University of Cambridge)

  • Daniel Ralph

    (Judge Business School, University of Cambridge)

Abstract

In most wholesale electricity markets generators must submit stepfunction offers of supply to a uniform price auction, and the market is cleared at the price of the most expensive offer needed to meet realised demand. Such markets can most elegantly be modelled as the purestrategy, Nash Equilibrium of continuous supply functions, in which each supplier has a unique profit maximising choice of supply function given the choices of other suppliers. Critics argue that the discreteness and discontinuity of the required steps can rule out pure-strategy equilibria and may result in price instability. This paper argues that if prices must be selected from a finite set the resulting step function converges to the continuous supply function as the number of steps increases, reconciling the apparently very disparate approaches to modelling electricity markets.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Pär Holmberg & David Newbery & Daniel Ralph, 2008. "Supply Function Equilibria: Step functions and continuous representations," Working Papers EPRG 0829, Energy Policy Research Group, Cambridge Judge Business School, University of Cambridge.
  • Handle: RePEc:enp:wpaper:eprg0829
    as

    Download full text from publisher

    File URL: https://www.eprg.group.cam.ac.uk/wp-content/uploads/2014/01/main-body3.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Natalia Fabra & Nils‐Henrik Fehr & David Harbord, 2006. "Designing electricity auctions," RAND Journal of Economics, RAND Corporation, vol. 37(1), pages 23-46, March.
    2. repec:rje:randje:v:37:y:2006:1:p:23-46 is not listed on IDEAS
    3. Frank A. Wolak, 2007. "Quantifying the supply-side benefits from forward contracting in wholesale electricity markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(7), pages 1179-1209.
    4. Robert Wilson, 2008. "Supply Function Equilibrium in a Constrained Transmission System," Operations Research, INFORMS, vol. 56(2), pages 369-382, April.
    5. Frank Wolak, 2000. "An Empirical Analysis of the Impact of Hedge Contracts on Bidding Behavior in a Competitive Electricity Market," International Economic Journal, Taylor & Francis Journals, vol. 14(2), pages 1-39.
    6. Holmberg, Pär, 2009. "Numerical calculation of an asymmetric supply function equilibrium with capacity constraints," European Journal of Operational Research, Elsevier, vol. 199(1), pages 285-295, November.
    7. Parisio, Lucia & Bosco, Bruno, 2003. "Market Power and the Power Market: Multi-unit Bidding and (In)Efficiency in Electricity Auctions," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 10(4), pages 377-401, August.
    8. 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.
    9. David M. Newbery, 1998. "Competition, Contracts, and Entry in the Electricity Spot Market," RAND Journal of Economics, The RAND Corporation, vol. 29(4), pages 726-749, Winter.
    10. Ilan Kremer & Kjell G. Nyborg, 2004. "Divisible-Good Auctions: The Role of Allocation Rules," RAND Journal of Economics, The RAND Corporation, vol. 35(1), pages 147-159, Spring.
    11. Green, Richard J, 1996. "Increasing Competition in the British Electricity Spot Market," Journal of Industrial Economics, Wiley Blackwell, vol. 44(2), pages 205-216, June.
    12. Anderson, Edward, 2011. "Supply Function Equilibria Always Exist," Working Papers 04/2011, University of Sydney Business School, Discipline of Business Analytics.
    13. Par Holmberg, 2007. "Supply Function Equilibrium with Asymmetric Capacities and Constant Marginal Costs," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2), pages 55-82.
    14. Ramteen Sioshansi & Shmuel Oren, 2007. "How good are supply function equilibrium models: an empirical analysis of the ERCOT balancing market," Journal of Regulatory Economics, Springer, vol. 31(1), pages 1-35, February.
    15. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 1-26.
    16. E. J. Anderson & H. Xu, 2004. "Nash equilibria in electricity markets with discrete prices," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(2), pages 215-238, October.
    17. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    18. David M. Newbery, 1995. "Power Markets and Market Power," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3), pages 39-66.
    19. Ali Hortaçsu & Steven L. Puller, 2008. "Understanding strategic bidding in multi‐unit auctions: a case study of the Texas electricity spot market," RAND Journal of Economics, RAND Corporation, vol. 39(1), pages 86-114, March.
    20. Ross Baldick & Ryan Grant & Edward Kahn, 2004. "Theory and Application of Linear Supply Function Equilibrium in Electricity Markets," Journal of Regulatory Economics, Springer, vol. 25(2), pages 143-167, March.
    21. von der Fehr, Nils-Henrik Morch & Harbord, David, 1993. "Spot Market Competition in the UK Electricity Industry," Economic Journal, Royal Economic Society, vol. 103(418), pages 531-546, May.
    22. Leo K. Simon, 1987. "Games with Discontinuous Payoffs," Review of Economic Studies, Oxford University Press, vol. 54(4), pages 569-597.
    23. Genc, Talat S. & Reynolds, Stanley S., 2011. "Supply function equilibria with capacity constraints and pivotal suppliers," International Journal of Industrial Organization, Elsevier, vol. 29(4), pages 432-442, July.
    24. Frank A. Wolak, 2001. "Identification and Estimation of Cost Functions Using Observed Bid Data: An Application to Electricity Markets," NBER Working Papers 8191, National Bureau of Economic Research, Inc.
    25. Jakub Kastl, 2011. "Discrete Bids and Empirical Inference in Divisible Good Auctions," Review of Economic Studies, Oxford University Press, vol. 78(3), pages 974-1014.
    26. David McAdams, 2003. "Isotone Equilibrium in Games of Incomplete Information," Econometrica, Econometric Society, vol. 71(4), pages 1191-1214, July.
    27. Robert Wilson, 1979. "Auctions of Shares," The Quarterly Journal of Economics, Oxford University Press, vol. 93(4), pages 675-689.
    28. repec:spr:compst:v:60:y:2004:i:2:p:215-238 is not listed on IDEAS
    29. Green, Richard J & Newbery, David M, 1992. "Competition in the British Electricity Spot Market," Journal of Political Economy, University of Chicago Press, vol. 100(5), pages 929-953, October.
    30. Supatgiat, Chonawee & Zhang, Rachel Q & Birge, John R, 2001. "Equilibrium Values in a Competitive Power Exchange Market," Computational Economics, Springer;Society for Computational Economics, vol. 17(1), pages 93-121, February.
    31. Andrew Sweeting, 2007. "Market Power In The England And Wales Wholesale Electricity Market 1995-2000," Economic Journal, Royal Economic Society, vol. 117(520), pages 654-685, April.
    32. Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-1277, November.
    33. Ilan Kremer, 2004. "Underpricing and Market Power in Uniform Price Auctions," Review of Financial Studies, Society for Financial Studies, vol. 17(3), pages 849-877.
    34. Bagh, Adib, 2010. "Variational convergence: Approximation and existence of equilibria in discontinuous games," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1244-1268, May.
    35. Aleksandr Rudkevich & Max Duckworth & Richard Rosen, 1998. "Modeling Electricity Pricing in a Deregulated Generation Industry: The Potential for Oligopoly Pricing in a Poolco," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3), pages 19-48.
    36. Kastl, Jakub, 2012. "On the properties of equilibria in private value divisible good auctions with constrained bidding," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 339-352.
    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. Anderson, Edward & Holmberg, Pär, 2018. "Price instability in multi-unit auctions," Journal of Economic Theory, Elsevier, vol. 175(C), pages 318-341.
    2. Pär Holmberg, 2017. "Pro‐competitive Rationing in Multi‐unit Auctions," Economic Journal, Royal Economic Society, vol. 127(605), pages 372-395, October.
    3. 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.
    4. de Frutos, Maria-Angeles & Fabra, Natalia, 2008. "On the Impact of Forward Contract Obligations in Multi-Unit Auctions," CEPR Discussion Papers 6756, C.E.P.R. Discussion Papers.
    5. Bolle, Friedel & Grimm, Veronika & Ockenfels, Axel & del Pozo, Xavier, 2013. "An experiment on supply function competition," European Economic Review, Elsevier, vol. 63(C), pages 170-185.
    6. Crawford, Gregory S. & Crespo, Joseph & Tauchen, Helen, 2007. "Bidding asymmetries in multi-unit auctions: Implications of bid function equilibria in the British spot market for electricity," International Journal of Industrial Organization, Elsevier, vol. 25(6), pages 1233-1268, December.
    7. Hunt Allcott, 2012. "The Smart Grid, Entry, and Imperfect Competition in Electricity Markets," NBER Working Papers 18071, National Bureau of Economic Research, Inc.
    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. de Frutos, María-Ángeles & Fabra, Natalia, 2012. "How to allocate forward contracts: The case of electricity markets," European Economic Review, Elsevier, vol. 56(3), pages 451-469.
    10. Kastl, Jakub, 2012. "On the properties of equilibria in private value divisible good auctions with constrained bidding," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 339-352.
    11. Xavier Vives, 2011. "Strategic Supply Function Competition With Private Information," Econometrica, Econometric Society, vol. 79(6), pages 1919-1966, November.
    12. Genc, Talat S. & Reynolds, Stanley S., 2011. "Supply function equilibria with capacity constraints and pivotal suppliers," International Journal of Industrial Organization, Elsevier, vol. 29(4), pages 432-442, July.
    13. Pär Holmberg & Andy Philpott, 2014. "Supply function equilibria in transportation networks," Cambridge Working Papers in Economics 1421, Faculty of Economics, University of Cambridge.
    14. Brown, David P. & Eckert, Andrew, 2021. "Analyzing firm behavior in restructured electricity markets: Empirical challenges with a residual demand analysis," International Journal of Industrial Organization, Elsevier, vol. 74(C).
    15. Fiuza de Bragança, Gabriel Godofredo & Daglish, Toby, 2016. "Can market power in the electricity spot market translate into market power in the hedge market?," Energy Economics, Elsevier, vol. 58(C), pages 11-26.
    16. Jorge Balat & Juan E. Carranza & Juan D. Martin, 2015. "Dynamic and Strategic Behavior in Hydropower-Dominated Electricity Markets: Empirical Evidence for Colombia," Borradores de Economia 886, Banco de la Republica de Colombia.
    17. 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.
    18. Holmberg, Par, 2008. "Unique supply function equilibrium with capacity constraints," Energy Economics, Elsevier, vol. 30(1), pages 148-172, January.
    19. Ali Hortaçsu & Steven L. Puller, 2008. "Understanding strategic bidding in multi‐unit auctions: a case study of the Texas electricity spot market," RAND Journal of Economics, RAND Corporation, vol. 39(1), pages 86-114, March.
    20. Bustos-Salvagno, Javier, 2015. "Bidding behavior in the Chilean electricity market," Energy Economics, Elsevier, vol. 51(C), pages 288-299.

    More about this item

    Keywords

    Auctions; supply function equilibria; convergence of step-functions; electricity markets;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • L94 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Electric Utilities

    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:enp:wpaper:eprg0829. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/jicamuk.html .

    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: Ruth Newman (email available below). General contact details of provider: https://edirc.repec.org/data/jicamuk.html .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.