The Optimal Design of First-Price Auctions with Financial Constraints and Default Risks

Abstract

If the bidders in an auction have financial constraints, how should the seller design the auction to maximize his profit? An observed practice is that the seller offers a loan, or interest subsidy, to the highest bidder. The work by Che and Gale [3] has given a partial answer for second-price auctions, with default risk assumed. away. This paper provides a complete solution for first-price auctions, with default risk included. For each level of the interest subsidy, we solve the auction game and give a closed form solution for its symmetric equilibrium. From this we determine each bidder's behavior as a function of the interest charged by the seller. This behavior exhibits the following novel bifurcation: for low interest rates, poor firms bid high and rich firms bid low; for high interest rates, the reverse is true. At the "critical" rate, bids from poor and rich firms are identical. From the seller's point of view, we obtain a formula showing expected profit as a function of the interest subsidy. This allows computation of a best subsidy. We show that the best rate is always larger than the critical rate. These results are especially applicable to auctions of large projects, where bidders' financial constraints are significant. (The FCC C-block auction is a recent example.)