"Optimal Scaling Auctions: A Consumer Theory Deconstruction"

(with Allan Hernandez-Chanto)

We study scaling auctions for procurement environments where sellers are risk-averse and have private fixed costs. We show that sellers' bidding behavior can be obtained as the solution to an auxiliary Hicksian demand problem in which the weights of the scoring rule serve as prices. Consequently, changes in weights induce a pure substitution effect, rationalizing the skewed bidding behavior observed in the empirical literature. Utilizing the Hicksian properties of equilibrium bidding, we characterize the scaling auctions that minimize the buyer's expected payment. Furthermore, we conduct a comparative analysis between scaling auctions and cash auctions, demonstrating that scaling auctions reduce the buyer's expected payment when sellers incur relatively large marginal costs. Lastly, we establish that a hybrid format outperforms both pure scaling and cash auction formats.