Journal of Regulatory Economics

, Volume 36, Issue 2, pp 154–177 | Cite as

Supply function equilibria of pay-as-bid auctions

  • Pär HolmbergEmail author
Original Article


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 for a one shot game. Existence of an equilibrium is ensured if the hazard rate of the demand distribution is monotonically decreasing with respect to the shock outcome 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 behavior 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.


Supply function equilibrium Pay-as-bid auction Discriminatory auction Divisible good auction Oligopoly Electricity market 

JEL Classifications (2000)

C62 D43 D44 L11 L13 L94 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Research Institute of Industrial EconomicsStockholmSweden

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