Third-Party Data Providers Ruin Simple Mechanisms

This paper studies the revenue of simple mechanisms in settings where a third-party data provider is present. When no data provider is present, it is known that simple mechanisms achieve a constant fraction of the revenue of optimal mechanisms. The results in this paper demonstrate that this is no longer true in the presence of a third party data provider who can provide the bidder with a signal that is correlated with the item type. Specifically, we show that even with a single seller, a single bidder, and a single item of uncertain type for sale, pricing each item-type separately (the analog of item pricing for multi-item auctions) and bundling all item-types under a single price (the analog of grand bundling) can both simultaneously be a logarithmic factor worse than the optimal revenue. Further, in the presence of a data provider, item-type partitioning mechanisms—a more general class of mechanisms which divide item-types into disjoint groups and offer prices for each group—still cannot achieve within a log log factor of the optimal revenue.