Auction Design for Bidders with Ex Post ROI Constraints

Motivated by practical constraints in online advertising, we investigate single-parameter auction design for bidders with constraints on their Return On Investment (ROI) -- a targeted minimum ratio between the obtained value and the payment. We focus on ex post ROI constraints, which require the ROI condition to be satisfied for every realized value profile. With ROI-constrained bidders, we first provide a full characterization of the allocation and payment rules of dominant-strategy incentive compatible (DSIC) auctions. In particular, we show that given any monotone allocation rule, the corresponding DSIC payment should be the Myerson payment with a rebate for each bidder to meet their ROI constraints. Furthermore, we also determine the optimal auction structure when the item is sold to a single bidder under a mild regularity condition. This structure entails a randomized allocation scheme and a first-price payment rule, which differs from the deterministic Myerson auction and previous works on ex ante ROI constraints.