Numerical calculation of an asymmetric supply function equilibrium with capacity constraints
Producers submit offer curves to a procurement auction, e.g. an electricity auction, before uncertain demand has been realised. In the supply function equilibrium (SFE), every firm commits to the offer curve that maximises its expected profit, given the offer curves of competitors. The equilibrium is given by a system of differential equations. In practice, it has been very difficult to find valid SFE, i.e. non-decreasing solutions, from this system, especially for asymmetric producers. This paper shows that valid SFE can be calculated by means of a shooting algorithm that combines numerical integration with an optimisation procedure that searches for an end-condition. Multiple/parallel shooting is used for ill-conditioned cases.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-77, November.
- 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.
- 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, 03.
- Bolle, Friedel, 1992. "Supply function equilibria and the danger of tacit collusion : The case of spot markets for electricity," Energy Economics, Elsevier, vol. 14(2), pages 94-102, April.
- 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.
- Borenstein, Severin & Bushnell, James & Knittel, Chris, 1999.
"Market Power in Electricity Markets: Beyond Concentration Measures,"
Staff General Research Papers
31548, Iowa State University, Department of Economics.
- Severin Borenstein & James Bushnell & Christopher R. Knittel, 1999. "Market Power in Electricity Markets: Beyond Concentration Measures," The Energy Journal, International Association for Energy Economics, vol. 0(Number 4), pages 65-88.
- 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 929-53, October.
- Green, Richard & Newbery, David M G, 1991. "Competition in the British Electricity Spot Market," CEPR Discussion Papers 557, C.E.P.R. Discussion Papers.
- Green, Richard J, 1996. "Increasing Competition in the British Electricity Spot Market," Journal of Industrial Economics, Wiley Blackwell, vol. 44(2), pages 205-16, June.
- von der Fehr, Nils-Henrik Morch & Harbord, David, 1993.
"Spot Market Competition in the UK Electricity Industry,"
Royal Economic Society, vol. 103(418), pages 531-46, May.
- Von der Fehr, N.H.M. & Harbord, D., 1992. "Spot Market Competition in the UK Electricity Industry," Memorandum 09/1992, Oslo University, Department of Economics.
- Holmberg, Pär, 2008. "Game-theoretical, Strategic forward Contracting in the Electricity Market," Working Paper Series 756, Research Institute of Industrial Economics.
- Holmberg, Par, 2008.
"Unique supply function equilibrium with capacity constraints,"
Elsevier, vol. 30(1), pages 148-172, January.
- Holmberg, Pär, 2004. "Unique Supply Function Equilibrium with Capacity Constraints," Working Paper Series 2004:20, Uppsala University, Department of Economics.
- Day, Christopher J & Bunn, Derek W, 2001. "Divestiture of Generation Assets in the Electricity Pool of England and Wales: A Computational Approach to Analyzing Market Power," Journal of Regulatory Economics, Springer, vol. 19(2), pages 123-41, March.
- Holmberg, Pär, 2005. "Asymmetric Supply Function Equilibrium with Constant Marginal Costs," Working Paper Series 2005:16, Uppsala University, Department of Economics.
When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:199:y:2009:i:1:p:285-295. 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: (Zhang, Lei)
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.