Mixed Strategies in Discriminatory Divisible-Good Auctions
73 Pages Posted: 22 Sep 2010 Last revised: 2 Feb 2011
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: Suggested Citation