Does Information Revelation Improve Revenue?

We study the problem of optimal auction design in a valuation model, explicitly motivated by online ad auctions, in which there is two-way informational asymmetry, in the sense that private information is available to both the seller (the item type) and the bidders (their type), and the value of each bidder for the item depends both on his own and the item's type. Importantly, we allow arbitrary auction formats involving, potentially, several rounds of signaling from the seller and decisions by the bidders, and seek to find the optimum co-design of signaling and auction (we call this optimum the "optimum augmented auction"). We characterize exactly the optimum augmented auction for our valuation model by establishing its equivalence with a multi-item Bayesian auction with additive bidders. Surprisingly, in the optimum augmented auction there is no signaling whatsoever, and in fact the seller need not access the available information about the item type until after the bidder chooses his bid. Suboptimal solutions to this problem, which have appeared in the recent literature, are shown to correspond to well-studied ways to approximate multi-item auctions by simpler formats, such as grand-bundling (this corresponds to Myerson's auction without any information revelation), selling items separately (this corresponds to Myerson's auction preceded by full information revelation as in [Fu et al. 2012]), and fractional partitioning (this corresponds to Myerson's auction preceded by optimal signaling). Consequently, all these solutions are separated by large approximation gaps from the optimum revenue.