Working Paper No. 787

Supply Function Equilibria of Pay-as-Bid Auctions

Published: January 29, 2009Pages: 30Keywords: Supply Function Equilibrium; Pay-as-bid Auction; Discriminatory Auction; DivisibleJEL-codes: C62; D43; D44; L11; L13; L94

Supply Function Equilibria of Pay-as-Bid Auctions Pär Holmberg

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.

Pär Holmberg


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Sick of Inequality?

An Introduction to the Relationship between Inequality and Health

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In this book Andreas Bergh, Therese Nilsson, IFN and Lund University, and Daniel Waldenström, IFN and Paris School of Economics, France, review the latest research on the relationship between inequality and health. What does inequality mean for our health? Does increasing income inequality affect outcomes such as obesity, life expectancy and subjective well-being?


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