On Revenue Maximization for Agents with Costly Information Acquisition

A prevalent assumption in traditional mechanism design is that buyers know their precise value for an item; however, this assumption is rarely true in practice. In most settings, buyers can "deliberate", i.e., spend money or time, in order improve their estimate of an item's value. It is known that the deliberative setting is fundamentally different than the classical one, and desirable properties of a mechanism such as equilibria, revenue maximization, or truthfulness, may no longer hold. In this paper we introduce a new general deliberative model in which users have independent private values that are a-priori unknown, but can be learned. We consider the design of dominant-strategy revenue-optimal auctions in this setting. Surprisingly, for a wide class of environments, we show the optimal revenue is attained with a sequential posted price mechanism (SPP). While this result is not constructive, we show how to construct approximately optimal SPPs in polynomial time. We also consider the design of Bayes-Nash incentive compatible auctions for a simple deliberative model.