Bidding à la Hicks: Which scoring rule is optimal for infrastructure procurement auctions?

Infrastructure projects are notoriously unpredictable. When governments auction these projects to private firms, who should bear these risks? Which auction format should the government use? How can they employ taxpayer money efficiently?

Scaling auctions (also known as unit-price auctions) are procurement mechanisms where firms bid unit prices for each task in a project, with the lowest weighted score winning. The winning firm is paid based on actual quantities used during construction allowing firms to transfer some quantity risk to the government.

In our recent paper, "Scaling Auctions in Procurement Settings with Risk-Averse Sellers," Allan Hernandez and I investigate how different scoring rules distribute financial risk between governments and construction firms. We show that bidding behavior in scaling auctions takes a simple form: bids follow an auxiliary Hicksian demand in which scoring weights act as prices, explaining the "skewed bidding" phenomenon often observed in empirical studies. Our most main finding is that the optimal scoring rule uses weights proportional to expected quantities—exactly what governments have been using.

Through this framework, we show that scaling auctions (where firms bid unit prices) outperform cash auctions (where firms bid fixed amounts) when marginal costs are sufficiently high relative to fixed costs. We also identify a hybrid auction format that outperforms both formats by allowing firms to optimally hedge against project risks.

Our findings provide clear guidance to government procurement agencies on when to use each auction format based on project characteristics. One the one hand we show that governments have used the optimal scoring rule. On the other hand though, we challenge the current practice of prohibiting bid skewing.

Working paper: Pdf

Abstract: We study scaling auctions in procurement settings with risk-averse sellers, showing that bidding behavior follows an auxiliary Hicksian demand in which scoring weights act as prices. As a result, changes in weights induce a pure substitution effect, providing a rationale for skewed bidding behavior observed in empirical studies. By using the Hicksian properties, we characterize the optimal scaling auction and show that it outperforms cash auctions if and only if marginal costs are sufficiently high. Additionally, we identify a hybrid auction format that outperforms both scaling and cash auctions.