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

Auction Design for Bidders with Ex Post ROI Constraints