2014/04/04 by Nima Haghpanah, Haghpanah, Nima, Jason D. Hartline +1 · 2 citations
Business, Management and Accounting · Decision Sciences · Economics, Econometrics and Finance · #Auction Theory and Applications #Computer Science and Game Theory (cs.GT) #Consumer Market Behavior and Pricing #FOS: Computer and information sciences #Merger and Competition Analysis
paper · pdf · doi:10.48550/arxiv.1404.1341
openalex publication_date 2014/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a multi-dimensional screening problem of selling a product with multiple quality levels and design virtual value functions to derive conditions that imply optimality of only selling highest quality. A challenge of designing virtual values for multi-dimensional agents is that a mechanism that pointwise optimizes virtual values resulting from a general application of integration by parts is not incentive compatible, and no general methodology is known for selecting the right paths for integration by parts. We resolve this issue by first uniquely solving for paths that satisfy certain necessary conditions that the pointwise optimality of the mechanism imposes on virtual values, and then identifying distributions that ensure the resulting virtual surplus is indeed pointwise optimized by the mechanism. Our method of solving for virtual values is general, and as a second application we use it to derive conditions of optimality for selling only the grand bundle of items to an agent with additive preferences.