Optimal Design of Scoring Auction with Multidimensional Quality

Abstract

This article studies the optimal design of scoring auctions used in public and private procurement. In this auction, each supplier's offer consists of both price and quality, and a supplier whose offer achieves the highest score wins. The environment we consider has the feature that quality is multidimensional, and the cost complementarity or cost substitutability among quality attributes significantly affects the form of a scoring rule which implements the buyer's optimal mechanism. Our results show that the optimal scoring rule can be additively separable in the quality attributes if the degree of cost substitutability between the attributes is nonpositive, and it cannot be additively separable if the degree is sufficiently high. An example shows how to compute the buyer's loss from using an additively separable scoring rule. We also investigate how the optimal scoring rule depends on the buyer's weight parameter on suppliers' profits and the number of suppliers.