Selling Evidence Bit by Bit

Abstract

We study the sale of an asset to competitive buyers. Before the sale, the seller can buy hard information about the asset from an intermediary who designs and prices a test to maximize his revenue guarantee across equilibria. The test consists of one or more signals, and the seller privately chooses which subset of signals to buy and selectively discloses their realization to the buyers. We show that the intermediary benefits from splitting information into multiple signals and characterize his maximal revenue guarantee as the cumulative entropy of the asset value distribution. This guarantee is achieved by a sequence of ``skim from the top'' tests with binary, i.i.d.\ signals and additive pricing. Furthermore, any sequence of tests that achieves the maximal guarantee reveals the asset's value in the limit. For binary values, we also characterize the revenue guarantee for any given number of signals, and show that it is achieved by a test that corresponds to a ``Swiss cheese" model of failure with conclusive good news.