Mixed strategies in discriminatory divisible-good auctions ∗

We introduce the concept of an offer distribution function to analyze randomized offer curves in multi-unit 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 we also characterize novel mixtures over partly increasing supply functions. We show that the randomization can cause considerable production inefficiencies.