Dynamic Mechanism Design with Budget Constrained Buyers Under Limited Commitment

Abstract

We study the dynamic mechanism design problem of a seller that repeatedly auctions independent items over a discrete time horizon to buyers that face a cumulative budget constraint. A driving motivation behind our model is the emergence of real-time bidding markets for online display advertising in which such budgets are prevalent. We assume the seller has a strong form of limited commitment: she commits to the rules of the current auction but cannot commit to those of future auctions. We show that the celebrated Myersonian approach that leverages the envelope theorem fails in this setting, and therefore, characterizing the dynamic optimal mechanism appears intractable. In turn, we make three main contributions. First, we show that the Myersonian approach is recovered in a corresponding fluid continuous-time model in which the time interval between consecutive items becomes negligible. Second, we leverage this approach to characterize the optimal dynamic direct-revelation mechanism, highlighting novel incentives at play in settings with buyers' budget constraints and seller's limited commitment. Third, we provide theoretical results that provide support for using the prescription arising from the fluid continuous-time model in the original discrete-time model.