Optimal Auction Design for Constrained Buyers

Abstract

We study single-parameter, multi-buyer auctions in which buyers are subject to constraints that affect their bidding strategy. Such constraints arise in many real-world auction settings and fundamentally alter the auction design space. As a consequence, the Revelation Principle, Envelope Theorem, and Myerson's Lemma no longer hold. In this paper we focus on a large family of buyer constraints where the buyers are restricted in the manner in which they can bid or spend their budget, but do not have a hard budget cap. These include the common constraints of no-overbidding, ex-post individual rationality, and stagewise individual rationality. We ask whether the seller can leverage the buyers' constraints to obtain improved payoff. Our main finding is a separation between \emph{revenue-aligned} seller objectives (e.g., revenue maximization, welfare, or any linear combination of the two), and \emph{consumer-aligned} seller objectives, which are objectives where the seller prefers \emph{lower} payments, e.g.~to maximize consumer surplus. For revenue-aligned objectives, we establish a unified theory for all constraints in the family, which parallels Myerson's theory of optimal auctions for unconstrained buyers. We develop a new measure-theoretic technique to show that Myerson-style auctions remain optimal, despite the altered design space and failure of the classical theory's central tenets. For consumer-aligned objectives, the picture is different: we show that the seller can leverage the buyers' strategic limitations to strictly outperform classically incentive compatible mechanisms. We design an optimal deterministic auction for a wide class of instances, focusing in particular on buyers who cannot tolerate temporary debt.