Optimal Auctions for Multi-Unit Procurement with Volume Discount Bids

Abstract

Our attention is focused on designing an optimal procurement mechanism which a buyer can use for procuring multiple units of a homogeneous item based on bids submitted by autonomous, rational, and intelligent suppliers. We design elegant optimal procurement mechanisms for two different situations. In the first situation, each supplier specifies the maximum quantity that can be supplied together with a per unit price. For this situation, we design an optimal mechanism S-OPT (Optimal with Simple bids). In the more generalized case, each supplier specifies discounts based on the volume of supply. In this case, we design an optimal mechanism VD-OPT (Optimal with Volume Discount bids). The VD-OPT mechanism uses the S-OPT mechanism as a building block. The proposed mechanisms minimize the cost to the buyer, satisfying at the same time, (a) Bayesian incentive compatibility and (b) interim individual rationality.