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Numerical calculation of an asymmetric supply function equilibrium with capacity constraints

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  • Holmberg, Pär

Abstract

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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Bibliographic Info

Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 199 (2009)
Issue (Month): 1 (November)
Pages: 285-295

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Handle: RePEc:eee:ejores:v:199:y:2009:i:1:p:285-295

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Web page: http://www.elsevier.com/locate/eor

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Keywords: Auctions/bidding Game theory OR in energy Supply function equilibrium Numerical integration Shooting;

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References

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  1. 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 531-46, May.
  2. 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.
  3. 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.
  4. Holmberg, Par, 2008. "Unique supply function equilibrium with capacity constraints," Energy Economics, Elsevier, vol. 30(1), pages 148-172, January.
  5. Holmberg, Pär, 2005. "Asymmetric Supply Function Equilibrium with Constant Marginal Costs," Working Paper Series 2005:16, Uppsala University, Department of Economics.
  6. Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-77, November.
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Citations

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Cited by:
  1. Holmberg, Par, 2008. "Unique supply function equilibrium with capacity constraints," Energy Economics, Elsevier, vol. 30(1), pages 148-172, January.
  2. Talat S. Genc & Stanley S. Reynolds, 2010. "Supply Function Equilibria with Capacity Constraints and Pivotal Suppliers," Working Papers 1007, University of Guelph, Department of Economics and Finance.
  3. Jie Chen, 2006. "The Dynamics of Housing Allowance Claims in Sweden: A Discrete Time-Hazard Analysis," International Journal of Housing Policy, Taylor & Francis Journals, vol. 6(1), pages 1-29.
  4. Holmberg, P. & Newbery, D & Ralph, D., 2008. "Supply Function Equilibria: Step Functions and Continuous Representations," Cambridge Working Papers in Economics 0863, Faculty of Economics, University of Cambridge.
  5. Holmberg, P. & Newbery, D., 2010. "The Supply Function Equilibrium and its Policy Implications for Wholesale Electricity Auctions," Cambridge Working Papers in Economics 1016, Faculty of Economics, University of Cambridge.
  6. Hallberg, Daniel, 2006. "Cross-national differences in income poverty among Europe´s 50+," Working Paper Series 2006:14, Uppsala University, Department of Economics.
  7. Engström, Per & Holmlund, Bertil, 2006. "Tax Evasion and Self-Employment in a High-Tax Country: Evidence from Sweden," Working Paper Series 2006:12, Uppsala University, Department of Economics.
  8. Newbery, D, 2008. "Analytic Solutions for Supply Function Equilibria: Uniqueness and Stability," Cambridge Working Papers in Economics 0848, Faculty of Economics, University of Cambridge.
  9. Johansson, Fredrik & Klevmarken, Anders, 2006. "Explaining the size and nature of response in a survey on health status and economic standard," Working Paper Series 2006:2, Uppsala University, Department of Economics.
  10. 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.
  11. Ollikka, Kimmo & Tukiainen , Janne, 2013. "Central bank liquidity auction mechanism design and the interbank market," Research Discussion Papers 21/2013, Bank of Finland.
  12. Holmberg, Pär, 2005. "Comparing Supply Function Equilibria of Pay-as-Bid and Uniform-Price Auctions," Working Paper Series 2005:17, Uppsala University, Department of Economics.
  13. Berg, Lennart & Berger, Tommy, 2005. "The Q theory and the Swedish housing market –an empirical test," Working Paper Series 2005:19, Uppsala University, Department of Economics.

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