Clinching Auction with Online Supply

Auctions for perishable goods such as internet ad in-ventory need to make real-time allocation and pricingdecisions as the supply of the good arrives in an on-line manner, without knowing the entire supply in ad-vance. These allocation and pricing decisions get com-plicated when buyers have some global constraints. Inthis work, we consider a multi-unit model where buyershave global budget constraints, and the supply arrivesin an online manner. Our main contribution is to showthat for this setting there is an individually-rational,incentive-compatible and Pareto-optimal auction thatallocates these units and calculates prices on the fly,without knowledge of the total supply. We do so byshowing that the Adaptive Clinching Auction satisfies asupply-monotonicity property.We also analyze and discuss, using examples, howthe insights gained by the allocation and payment rulecan be applied to design better ad allocation heuristicsin practice. Finally, while our main technical resultconcerns multi-unit supply, we propose a formal modelof online supply that captures scenarios beyond multi-unit supply and has applications to sponsored search.We conjecture that our results for multi-unit auctionscan be extended to these more general models.