Design of Divisible Good Auctions

This paper studies the relative performance of various formats for selling divisible goods. We analyze the two most common auction formats, the uniform price and discriminatory price designs, and contrast them with the Vickrey and the optimal mechanisms. We derive and characterize the unique linear Bayesian Nash equilibria in small and large auctions. We establish revenue rankings of the four auction formats for different risk preferences of the bidders and the auctioneer. We further address the questions that have been raised in practical design of auctioning divisible goods, such as fostering more aggressive bidding, increasing transparency, and stabilizing prices. In a model with endogenous entry, we also examine the problem of encouraging bidder participation in different designs.