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Songzi DuAssistant Professor Songzi Du on Auctions

Auctions have been an important method in allocating goods in the economy. Poorly designed auctions, ones that can be manipulated by bidders or result in poor allocations of the goods given preferences, can do more harm than good. So economists have devoted a lot of time to thinking carefully about how to design auction markets that work well. UCSD microeconomic theorist Songzi Du has extended our knowledge of auctions in a paper published in the May 2021 issue of Econometrica. Instead of looking for the auction that works best in a specific environment (what is specified are details of the preferences of the bidders, what different bidders believes about each others’ valuations, what they believe about each others’ beliefs, etc), Songzi looks for auctions that work well in a wide range of circumstances.

This paper studies profit-maximizing auction design when bidders have a common value for the good, but partial and differential information about that value. The paper takes a robustness approach, by now a well-established theme in the literature: The seller knows the distribution of the common value, but does not know the exact properties of the bidders’ information about that value and each other’s beliefs thereof; moreover, the seller evaluates each auction according to the lowest expected profit across all specifications of the bidders’ information (profit guarantee).

The paper solves the optimal auction that maximizes the profit guarantee, which takes the form of a proportional auction: each bidder submits a one-dimensional bid, the aggregate allocation and aggregate payment depend on the aggregate bid, and individual allocations and payments are proportional to bids. This kind of auction is reminiscent of the “voucher” auctions used to privatize Soviet state assets in the 1990s, where one bids in vouchers and receives a share of the asset that is proportional to one’s bid. The paper shows that the proportional allocation and payment rules optimally hedge against the uncertainty in the informational environment and maximizes the seller’s profit even in the worst case.