Scandinavian Working Papers in Economics

Working Paper Series,
Research Institute of Industrial Economics

No 814: Mixed Strategies in Discriminatory Divisible-good Auctions

Edward J. Anderson, Pär Holmberg () and Andrew B. Philpott
Additional contact information
Edward J. Anderson: Faculty of Economics and Business, Postal: University of Sydney, Australia
Pär Holmberg: Research Institute of Industrial Economics (IFN), Postal: P.O. Box 55665, SE-102 15 Stockholm, Sweden
Andrew B. Philpott: Department of Engineering Science, Postal: University of Auckland, Australia

Abstract: Author: Edward J. Anderson, Pär Holmberg and Andrew B. Philpott Keywords: Pay-as-bid Auction; Divisible Good Auction; Mixed Strategy Equilibria; Wholesale Electricity Markets Pages: 71 Published: November 24, 2009 JEL-codes: D43; D44; C72 Download Wp814.pdf (756 kB) Abstract Using the concept of market-distribution functions, we derive general optimality conditions for discriminatory divisible-good auctions, which are also applicable to Bertrand games and non-linear pricing. We introduce the concept of offer distribution function to analyze randomized offer curves, and characterize mixed-strategy Nash equilibria for pay-as-bid auctions where demand is uncertain and costs are common knowledge; a setting for which pure-strategy supply function equilibria typically do not exist. We generalize previous results on mixtures over horizontal offers as in Bertrand-Edgeworth games, but more importantly we characterize novel mixtures over partly increasing supply functions.

Keywords: Pay-as-bid Auction; Divisible Good Auction; Mixed Strategy Equilibria; Wholesale Electricity Markets

JEL-codes: C72; D43; D44

71 pages, November 24, 2009

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Published as
Edward J. Anderson, Pär Holmberg and Andrew B. Philpott, (2013), 'Mixed Strategies in Discriminatory Divisible-good Auctions', Rand Journal of Economics, vol 44, no 1, pages 1-32

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