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Supply function equilibria of pay-as-bid auctions

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  • Pär Holmberg

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Abstract

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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Bibliographic Info

Article provided by Springer in its journal Journal of Regulatory Economics.

Volume (Year): 36 (2009)
Issue (Month): 2 (October)
Pages: 154-177

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Handle: RePEc:kap:regeco:v:36:y:2009:i:2:p:154-177

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Web page: http://www.springerlink.com/link.asp?id=100298

Related research

Keywords: Supply function equilibrium; Pay-as-bid auction; Discriminatory auction; Divisible good auction; Oligopoly; Electricity market; C62; D43; D44; L11; L13; L94;

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References

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  1. 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.
  2. 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.
  3. Holmberg, Pär, 2004. "Unique Supply Function Equilibrium with Capacity Constraints," Working Paper Series 2004:20, Uppsala University, Department of Economics.
  4. 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.
  5. Paul Klemperer, 2002. "What Really Matters in Auction Design," Journal of Economic Perspectives, American Economic Association, vol. 16(1), pages 169-189, Winter.
  6. Alfred E. Kahn & Peter Cramton & Robert H. Porter & Richard D. Tabors, 2001. "Uniform Pricing or Pay-as-Bid Pricing: A Dilemma for California and Beyond," Papers of Peter Cramton 01ej, University of Maryland, Department of Economics - Peter Cramton, revised 27 Jan 2001.
  7. 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.
  8. 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.
  9. Wilson, Robert, 1997. "Nonlinear Pricing," OUP Catalogue, Oxford University Press, number 9780195115826, September.
  10. Wilson, Robert B., 2007. "Supply Function Equilibrium in a Constrained Transmission System," Research Papers 1966, Stanford University, Graduate School of Business.
  11. 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.
  12. 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.
  13. Bulow, Jeremy & Klemperer, Paul, 1996. "Auctions versus Negotiations," American Economic Review, American Economic Association, vol. 86(1), pages 180-94, March.
  14. 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.
  15. repec:rne:rneart:v:4:y:2005:i:2:p:93-128 is not listed on IDEAS
  16. Natalia Fabra, 2003. "Tacit Collusion in Repeated Auctions: Uniform Versus Discriminatory," Journal of Industrial Economics, Wiley Blackwell, vol. 51(3), pages 271-293, 09.
  17. 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.
  18. 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.
  19. 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. Heim, Sven & Götz, Georg, 2013. "Do pay-as-bid auctions favor collusion? Evidence from Germany's market for reserve power," ZEW Discussion Papers 13-035, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
  2. Ollikka, Kimmo & Tukiainen , Janne, 2013. "Central bank liquidity auction mechanism design and the interbank market," Research Discussion Papers 21/2013, Bank of Finland.
  3. Holmberg, P. & Willems, Bert, 2012. "Relaxing Competition through Speculation: Committing to a Negative Supply Slope," Discussion Paper 2012-088, Tilburg University, Center for Economic Research.
  4. Holmberg, Pär & Newbery, David, 2009. "The Supply Function Equilibrium and Its Policy Implications for Wholesale Electricity Auctions," Working Paper Series 812, Research Institute of Industrial Economics.
  5. Majid Motamedi & Shahram Moeeni & Salman Gharakhani & Iman Keyfarokhi, 2014. "The Behavior of Iranian Restructured Electricity Market in Supply Function Equilibrium Framework," International Journal of Academic Research in Business and Social Sciences, Human Resource Management Academic Research Society, International Journal of Academic Research in Business and Social Sciences, vol. 4(1), pages 178-191, January.

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