  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 values. Assuming that the seller adopts
the optimal auction due to Myerson (1981) in response, we characterize both the
buyer-optimal information structure, which maximizes the buyers' surplus, and
the sellerworst information structure, which minimizes the seller's revenue. We
translate both information design problems into finite-dimensional, constrained
optimization problems in which one can explicitly solve for the optimal
information structures. In contrast to the case with one buyer (Roesler and
Szentes, 2017), we show that with two or more buyers, the symmetric
buyer-optimal information structure is different from the symmetric
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
symmetric 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 can generate a strictly higher surplus for the buyers than the
symmetric buyer-optimal information structure.
