Information Design in Optimal Auctions

Abstract

We study the information design problem in a single-unit auction setting. The information designer controls independent private signals according to which the buyers infer their binary private value. Assuming that the seller adopts Myerson (1981) optimal auction in response, we characterize both the buyer-optimal information structure which maximizes the buyers' surplus and the seller-worst information structure which minimizes the seller's revenue. We translate both information design problems into finite-dimensional constrained optimization problems for which the optimal information structures can be explicitly solved. In contrast to the case with one buyer (Roesler and Szentes, 2017 and Du, 2018), we show that with two or more buyers, the buyer-optimal information structure is different from the seller-worst information structure: the good is always sold under the seller-worst information structure but not under the buyer-optimal information structure. Nevertheless, as the number of buyers goes to infinity, both information structures converge to no disclosure. We also show that in an ex ante symmetric setting, an asymmetric information structure is never seller-worst but for some prior can generate a strictly higher surplus for the buyers than the symmetric buyer-optimal information structure.