Multi-unit auctions with budget limits

► We study multi-unit auctions for bidders with a budget constraint. We show: ► Any truthful and IR auction with no positive transfers cannot be Pareto optimal. ► However, the “clinching auction” satisfies all these properties with public budgets. ► Moreover, it is the unique such auction when there are two players. We study multi-unit auctions for bidders that have a budget constraint, a situation very common in practice that has received relatively little attention in the auction theory literature. Our main result is an impossibility: there is no deterministic auction that (1) is individually rational and dominant-strategy incentive-compatible, (2) makes no positive transfers, and (3) always produces a Pareto optimal outcome. In contrast, we show that Ausubelʼs “clinching auction” satisfies all these properties when the budgets are public knowledge. Moreover, we prove that the “clinching auction” is the unique auction that satisfies all these properties when there are two players. This uniqueness result is the cornerstone of the impossibility result. Few additional related results are given, including some results on the revenue of the clinching auction and on the case where the items are divisible.