Mixed Strategies in Discriminatory Divisible-Good Auctions

73 Pages Posted: 22 Sep 2010 Last revised: 2 Feb 2011

See all articles by Edward J. Anderson

Edward J. Anderson

University of Sydney Business School

Par Holmberg

Research Institute of Industrial Economics (IFN)

Andrew Philpott

University of Auckland - Department of Engineering Science

Date Written: April 28, 2010

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 o¤er 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, and we also characterize novel mixtures over partly increasing supply functions.

Keywords: Pay-as-Bid Auction, Divisible Good Auction, Mixed Strategy Equilibria, Wholesale Electricity Markets

JEL Classification: D43, D44, C72

Suggested Citation

Anderson, Edward J. and Holmberg, Par and Philpott, Andrew, Mixed Strategies in Discriminatory Divisible-Good Auctions (April 28, 2010). IFN Working Paper No. 814, Available at SSRN: https://ssrn.com/abstract=1679284 or http://dx.doi.org/10.2139/ssrn.1679284

Edward J. Anderson

University of Sydney Business School ( email )

Cnr. of Codrington and Rose Streets
Sydney, NSW 2006
Australia

Par Holmberg (Contact Author)

Research Institute of Industrial Economics (IFN) ( email )

Box 55665
Grevgatan 34, 2nd floor
Stockholm, SE-102 15
Sweden

Andrew Philpott

University of Auckland - Department of Engineering Science ( email )

Private Bag 92019
Auckland
New Zealand

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