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.
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- Holmberg, Pär, 2005. "Asymmetric Supply Function Equilibrium with Constant Marginal Costs," Working Paper Series 2005:16, 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 123-141, March.
- 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.
- Borenstein, Severin & Bushnell, James & Knittel, Chris, 1999. "Market Power in Electricity Markets: Beyond Concentration Measures," Staff General Research Papers Archive 31548, Iowa State University, Department of Economics.
- 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.
- Green, Richard & Newbery, David M G, 1991. "Competition in the British Electricity Spot Market," CEPR Discussion Papers 557, C.E.P.R. Discussion Papers.
- Holmberg, Par, 2008. "Unique supply function equilibrium with capacity constraints," Energy Economics, 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.
- Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
- Krishna, Vijay, 2002. "Auction Theory," Elsevier Monographs, Elsevier, edition 1, number 9780124262973.
- 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.
- 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.
- Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-1277, November.
- 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.
- 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.
- 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.
- 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.
- 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.
- Holmberg, Pär, 2008. "Game-theoretical, Strategic forward Contracting in the Electricity Market," Working Paper Series 756, Research Institute of Industrial Economics. Full references (including those not matched with items on IDEAS)
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