We introduce the concept of an offer distribution function to analyze randomized offer curves in multiunit procurement auctions. We 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 also characterize novel mixtures over partly increasing supply functions. We show that the randomization can cause considerable production inefficiencies.
Anderson, Edward J., Pär Holmberg and Andrew B. Philpott (2013),
"Mixed Strategies in Discriminatory Divisible-good Auctions".
RAND Journal of Economics