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Supply Function Equilibria of Pay-as-Bid Auctions

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  • Holmberg, Pär

    ()
    (Research Institute of Industrial Economics (IFN))

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

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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Keywords: Supply Function Equilibrium; Pay-as-bid Auction; Discriminatory Auction; Divisible;

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References

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  1. Paul Klemperer, 2002. "What Really Matters in Auction Design," Journal of Economic Perspectives, American Economic Association, vol. 16(1), pages 169-189, Winter.
  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. 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.
  4. 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.
  5. 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.
  6. Wilson, Robert, 1997. "Nonlinear Pricing," OUP Catalogue, Oxford University Press, number 9780195115826, September.
  7. Holmberg, Par, 2008. "Unique supply function equilibrium with capacity constraints," Energy Economics, Elsevier, vol. 30(1), pages 148-172, January.
  8. Natalia Fabra, 2003. "Tacit Collusion in Repeated Auctions: Uniform Versus Discriminatory," Journal of Industrial Economics, Wiley Blackwell, vol. 51(3), pages 271-293, 09.
  9. 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.
  10. Giulio Federico & David Rahman, 2000. "Bidding in an electricity pay-as-bid auction," Economics Papers 2001-W5, Economics Group, Nuffield College, University of Oxford, revised 01 Apr 2001.
  11. 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.
  12. 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.
  13. Wilson, Robert B., 2007. "Supply Function Equilibrium in a Constrained Transmission System," Research Papers 1966, Stanford University, Graduate School of Business.
  14. 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.
  15. Bulow, Jeremy & Klemperer, Paul, 1996. "Auctions versus Negotiations," American Economic Review, American Economic Association, vol. 86(1), pages 180-94, March.
  16. 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.
  17. 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.
  18. Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-77, November.
  19. repec:rne:rneart:v:4:y:2005:i:2:p:93-128 is not listed on IDEAS
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Citations

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Cited by:
  1. Holmberg, P. & Willems, B., 2012. "Relaxing competition through speculation: Committing to a negative supply slope," Cambridge Working Papers in Economics 1252, Faculty of Economics, University of Cambridge.
  2. 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.
  3. Holmberg, Pär & Newbery, David, 2010. "The supply function equilibrium and its policy implications for wholesale electricity auctions," Utilities Policy, Elsevier, vol. 18(4), pages 209-226, December.
  4. 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.
  5. Ollikka, Kimmo & Tukiainen , Janne, 2013. "Central bank liquidity auction mechanism design and the interbank market," Research Discussion Papers 21/2013, Bank of Finland.

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