Working Paper Series
Supply Function Equilibria of Pay-as-Bid Auctions
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; (follow links to similar papers)
JEL-Codes: C62; D43; D44; L11; L13; L94; (follow links to similar papers)
30 pages, January 29, 2009
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Full text versions of the paper:
- This paper is published as:
Holmberg, Pär, (2009), 'Supply Function Equilibria of Pay-as-Bid Auctions', Journal of Regulatory Economics, Vol. 36, pages 154-177
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