Optimal Auction Design for Constrained Buyers
Batya Berzack, Rotem Oshman, Inbal Talgam-Cohen
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: the revelation principle, envelope theorem, and Myerson's lemma no longer hold. Our focus is on a large family of constraints where the buyers do not have a hard budget-cap, but are restricted in how they can bid or spend their budget --- including no-overbidding, ex-post individual rationality (IR), and stagewise IR. We ask whether the seller can leverage the buyers' constraints to obtain improved payoff. We separate between \emph{revenue-aligned} seller objectives (revenue, welfare, or any linear combination), and \emph{consumer-aligned} seller objectives (e.g.\ consumer surplus). For the former, 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. In contrast, we show a consumer-aligned seller can leverage the buyers' strategic limitations to strictly outperform mechanisms that are classically incentive compatible. We also design an auction arbitrarily close to optimal for buyers who cannot tolerate temporary debt.
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