Problem definition: We consider the mechanism design problem of finding an optimal pay-as-bid mechanism in which the platform chooses an assortment of suppliers that balances 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 and private procurement, often consist of a single platform that intermediates transactions. Frequently, these platforms implement simple and transparent mechanisms to induce suppliers' direct participation, which typically result 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: For a broad class of symmetric models, we show the optimality of k-SRs. Additionally, we provide evidence of the robustness of k-SRs and of their extensions in more general 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 procurement settings.
