[UTMD-065] Beyond Quasilinearity: Exploring Nonlinear Scoring Rules in Procurement Auctions (by Makoto Hanazono, Jun Nakabayashi, Ryuji Sano, Masanori Tsuruoka)

Makoto Hanazono, Jun Nakabayashi, Ryuji Sano, Masanori Tsuruoka

This study examines procurement auctions in which bidders submit price and quality, and bids are evaluated using a price-per-quality-ratio (PQR) scoring rule. We formulate a model of scoring auctions in which bidder cost is determined by a unidimensional type and a unidimensional quality and then characterize the equilibrium bidding behavior for the first-score and second-score auctions. In contrast to well-known quasilinear scoring rules in which price and quality are additively separable and the score is linear in price, the equivalence theorem does not hold between the auction formats in our setup. We show that the second-score auction yields a lower (better) expected score than the first-score auction. We also provide a set of conditions under which expected quality and price are higher in the first-score auction than in the second-score auction. Finally, we show how these results can be extended to other non-quasilinear scoring rules.