Technical Note—Bidding in Multidimensional Auctions When the Qualities of All Bidders Matter

In multidimensional auctions, bidders compete in both quality and price, which are combined by a score rule. A well-known problem in procurement management is that nonprice attributes are often poorly measured and unreliably estimated. Adjustments of the reported quality based on the qualities of rival bids can enhance the reliability of the measurement process. We develop a general model of score function that is dependent on the qualities offered by all bidders who differ in terms of their production efficiency. We derive the ex ante equilibrium quality and price in a first-score and second-score auction environment when the cost is additive separable in terms of quality and production inefficiency. Bidders symmetrically select the quality that maximizes their margin for a given score, assuming that opponents act similarly. We demonstrate that the expected procurement cost is the same in the second-score auction and the first-score auction. We apply the findings in different forms of quality adjustments and show that the standard unadjusted auction yields the highest equilibrium quality and price, resulting in the highest expected procurement cost for the buyer. The findings could stimulate drastic changes in the conduct of procurement management, allowing the score rule to be determined by integrating all competing bidder qualities.