Scandinavian Working Papers in Economics

Working Paper Series,
Research Institute of Industrial Economics

No 787: Supply Function Equilibria of Pay-as-Bid Auctions

Pär Holmberg ()
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Pär Holmberg: Research Institute of Industrial Economics (IFN), Postal: P.O. Box 55665, SE-102 15 Stockholm, Sweden

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.

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

JEL-codes: C62; D43; D44; L11; L13; L94

30 pages, January 29, 2009

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