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Working Paper No. 814

Mixed Strategies in Discriminatory Divisible-good Auctions

Working Paper
Anderson, Edward J., Pär Holmberg and Andrew B. Philpott (2009). “Mixed Strategies in Discriminatory Divisible-good Auctions”. IFN Working Paper No. 814. Stockholm: Research Institute of Industrial Economics (IFN).

Edward J. Anderson, Pär Holmberg, Andrew B. Philpott

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.

Pär Holmberg

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