Price Caps and Scores in Multi-Object,Pay-As-Bid Procurement Auctions

Abstract

We study three multi-unit, pay-as-bid procurement auction formats where there is one buyer, N sellers, and the buyer has access to a signal of each seller’s opportunity cost. We begin with an analysis of the simple pay-as-bid format, for which we derive a closed-form solution. We then study a format with individual price-caps, where we study the impact of varying the price cap's tightness. Last, we consider two alternative formats based on scores and reference prices determined either exogenously or endogenously. For all formats but the first, we use combined analytical and numerical methods to characterize optimal bidding and equilibrium predictions. These auction formats are proposed in Cramton et al. (2019) as alternatives for the auctions of the Conservation Reserve Program (CRP) and studied empirically using a laboratory experiment. We calibrate our theoretical auction comparisons in terms of optimal bidding, equilibrium, efficiency, and cost-effectiveness matching the parameters used in the cited paper