Multi-Unit Bayesian Auction with Demand or Budget Constraints

In this work, we study multiple item auctions in a setting where items are distinguished by their relative values; any pair of items have the same ratio of values to all buyers. Buyers have additive valuations for multiple items. The application we have in mind is that items are positions in an ad auction, and an item’s value corresponds to its click-through rate. Buyers have various per-click valuations, which is their private information. We consider a Bayesian model for the values of buyers on the positions. We develop the optimal (maximum revenue) auction for a relaxed demand model (where each buyer i wants at most di items) and a sharp demand model (where buyer i wants exactly di items). We also find a 1/2 approximation for the case when the buyers are budget constrained.