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Supply Function Equilibria of Pay-as-Bid Auctions

This paper characterizes the Nash equilibrium in a pay-as-bid (discriminatory), divisible-good, procurement auction. Demand by the auctioneer is uncertain as in the supply function equilibrium model. A closed form expression is derived. Existence of an equilibrium is ensured if the hazard rate of the perfectly inelastic demand is monotonically decreasing and sellers have non-decreasing marginal costs. Multiple equilibria can be ruled out for markets, for which the auctioneer’s demand exceeds suppliers’ capacity with a positive probability. The derived equilibrium can be used to model strategic bidding behaviour in pay-as-bid electricity auctions, such as the balancing mechanism of United Kingdom. Offer curves and mark-ups of the derived equilibrium are compared to results for the SFE of a uniform-price auction.

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Paper provided by Research Institute of Industrial Economics in its series Working Paper Series with number 787.

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Length: 30 pages
Date of creation: 29 Jan 2009
Date of revision:
Publication status: Published as Holmberg, Pär, 'Supply Function Equilibria of Pay-as-Bid Auctions' in Journal of Regulatory Economics, 2009, pages 154-177.
Handle: RePEc:hhs:iuiwop:0787
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  1. Roques Fabien A. & Newbery David M. & Nuttall William J., 2005. "Investment Incentives and Electricity Market Design: the British Experience," Review of Network Economics, De Gruyter, vol. 4(2), pages 1-36, June.
  2. Holmberg, Pär, 2004. "Unique Supply Function Equilibrium with Capacity Constraints," Working Paper Series 2004:20, Uppsala University, Department of Economics.
  3. Professor Paul Klemperer, 2000. "What Really Matters in Auction Design," Microeconomics 0004008, EconWPA.
  4. Bower, John & Bunn, Derek, 2001. "Experimental analysis of the efficiency of uniform-price versus discriminatory auctions in the England and Wales electricity market," Journal of Economic Dynamics and Control, Elsevier, vol. 25(3-4), pages 561-592, March.
  5. Wilson, Robert B., 2007. "Supply Function Equilibrium in a Constrained Transmission System," Research Papers 1966, Stanford University, Graduate School of Business.
  6. Giulio Federico & David Rahman, 2001. "Bidding in an Electricity Pay-as-Bid Auction," Economics Series Working Papers 2001-W05, University of Oxford, Department of Economics.
  7. Kahn, Alfred E. & Cramton, Peter C. & Porter, Robert H. & Tabors, Richard D., 2001. "Uniform Pricing or Pay-as-Bid Pricing: A Dilemma for California and Beyond," The Electricity Journal, Elsevier, vol. 14(6), pages 70-79, July.
  8. Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-77, November.
  9. 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.
  10. 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.
  11. Rassenti, Stephen J & Smith, Vernon L & Wilson, Bart J, 2003. "Discriminatory Price Auctions in Electricity Markets: Low Volatility at the Expense of High Price Levels," Journal of Regulatory Economics, Springer, vol. 23(2), pages 109-23, March.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. Wilson, Robert, 1997. "Nonlinear Pricing," OUP Catalogue, Oxford University Press, number 9780195115826, March.
  17. repec:rne:rneart:v:4:y:2005:i:2:p:93-128 is not listed on IDEAS
  18. Bulow, Jeremy & Klemperer, Paul, 1996. "Auctions versus Negotiations," American Economic Review, American Economic Association, vol. 86(1), pages 180-94, March.
  19. Natalia Fabra, 2003. "Tacit Collusion in Repeated Auctions: Uniform Versus Discriminatory," Journal of Industrial Economics, Wiley Blackwell, vol. 51(3), pages 271-293, 09.
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