Pure Information Design in Classic Auctions


In many auction environments sellers are better informed about bidders' valuations than the bidders themselves. For such environments we derive a sharp and general optimal policy of information transmission in the case of independent private values. Under this policy bidders whose (ex-post) valuation is below a certain threshold are provided with all the information (about their valuations), but those bidders whose valuation lies below the threshold receive no information whatsoever. Surprisingly, the threshold expressed in percentiles is independent of the probability distribution over bidders' ex-post valuations; it depends solely on the number of bidders. Similar results are also derived for the bidder-optimal policy. Our analysis builds on the approach of Bayesian persuasion  and on a linearity of sellers' revenues as a function of the inverse distribution. This latter property allows us to use important results on stochastic comparisons.