The Design of Optimal Pay-as-Bid Procurement Mechanisms

Problem definition: We consider the mechanism design problem of finding an optimal pay-as-bid mechanism in which a platform chooses an assortment of suppliers to balance the tradeoff between two objectives: providing enough variety to accommodate heterogeneous buyers, yet at low prices. Academic/practical relevance: Modern buying channels, including e-commerce and public procurement, often consist of a platform that mediates transactions. Frequently, these platforms implement simple and transparent mechanisms to induce suppliers’ direct participation, which typically results in pay-as-bid (or first-price) mechanisms where suppliers set their prices. Methodology: We introduce a novel class of assortment mechanisms that we call k-soft reserves (k-SRs): If at least k suppliers choose a price below the soft-reserve price, then only those suppliers are added to the assortment; otherwise, all the suppliers are added. Results: We show the optimality of k-SRs for a class of stylized symmetric models to derive the intuition behind these mechanisms. Then, through extensive numerical simulations, we provide evidence of the robustness of k-SRs in more general and realistic settings. Managerial implications: Our results give intuitive and simple-to-use prescriptions on how to optimize pay-as-bid assortment mechanisms in practice, with an emphasis on public procurement settings. Funding: J. Choi thanks the Samsung Scholarship and Stanford Graduate School of Business for financial support. G. Weintraub thanks Joseph and Laurie Lacob for the support during the 2018–2019 academic year as a Joseph and Laurie Lacob Faculty Scholar at Stanford Graduate School of Business. Supplemental Material: The online appendices are available at https://doi.org/10.1287/msom.2022.1180 .