Clinching Auctions with Online Supply

Auctions for perishable goods such as internet ad inventory need to make real-time allocationand pricing decisions as the supply of the good arrives in an online manner, without knowing theentire supply in advance. These allocation and pricing decisions get complicated when buyershave some global constraints. In this work, we consider a multi-unit model where buyers haveglobal budget constraints, and the supply arrives in an online manner. Our main contribution isto show that for this setting there is an individually-rational, incentive-compatible and Pareto-optimal auction that allocates these units and calculates prices on the fly, without knowledge ofthe total supply. We do so by showing that the Adaptive Clinching Auction satisfies a supply-monotonicity property.We also analyze and discuss, using examples, how the insights gained by the allocation andpayment rule can be applied to design better ad allocation heuristics in practice. Finally, whileour main technical result concerns multi-unit supply, we propose a formal model of online supplythat captures scenarios beyond multi-unit supply and has applications to sponsored search. Weconjecture that our results for multi-unit auctions can be extended to these more general models.