In this paper, we study score procurement auctions with all-pay quality bids. A supplier’s score is the difference between his quality and price bids. The supplier with the highest score wins and gets paid his own price bid. The procurer’s payoff is the difference between the winner’s quality and the procurer’s payments to the suppliers. Equilibrium quality and price bids are solved without first obtaining the corresponding equilibrium scores. We find that quality bids, the suppliers’ payoffs and the procurer’s payoff do not depend on whether price bids are made contingent on quality bids. Compared to a benchmark of winner-pay quality bids, in which the losing suppliers’ quality bidding costs are reimbursed by the procurer, all-pay quality bids tend to reduce quality provision and suppliers' payoffs, but they tend to increase the total surplus and the procurer’s payoff.
Kovenock, D & Lu, J. (2020). All pay quality-bids in score procurement auctions. ESI Working Paper 20-01. https://digitalcommons.chapman.edu/esi_working_papers/293/