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Supply Function Equilibria of Pay-as-Bid Auctions

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Author Info
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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Publisher 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:
Handle: RePEc:hhs:iuiwop:0787

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

Find related papers by JEL classification:
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection
D44 - Microeconomics - - Market Structure and Pricing - - - Auctions
L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
L94 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Electric Utilities

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