Procurement Auctions with General Price-Quality Evaluation

We offer a general framework to study procurement auctions when quality matters. In this environment, sellers compete for a project by bidding a price-quality pair, and the winning bidder is determined by the score assigned to each bid. In contrast to the existing study in which only the quasilinear scoring rule is considered, our analysis allows a broad class of scoring rules including many other realistic ones. We focus on the analyses of the equilibrium bidding behavior of first-score (FS) and second-score (SS) auctions. We find that FS or SS auctions can be transformed into equivalent, single-dimensional score-bid auctions where the bidder's utility (payoff upon winning) is non-linear in the score-bid. Our analysis demonstrates that the ranking of the two auction formats, in terms of expected scores, depends on the scoring rule and that the equivalence fails unless scoring rules are quasilinear. FS auctions induce less aggressive bidding than SS auctions if, for example, the scoring rule is price-quality ratio (PQR).