2009/07/13 by Shaddin Dughmi, Dughmi, Shaddin, Hu Fu +3
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #Auction Theory and Applications #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #Game Theory and Voting Systems #Optimization and Search Problems
paper · pdf · doi:10.48550/arxiv.0907.1948
openalex publication_date 2009/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If a two-player social welfare maximization problem does not admit a PTAS, we prove that any maximal-in-range truthful mechanism that runs in polynomial time cannot achieve an approximation factor better than 1/2. Moreover, for the k-player version of the same problem, the hardness of approximation improves to 1/k under the same two-player hardness assumption. (We note that 1/k is achievable by a trivial deterministic maximal-in-range mechanism.) This hardness result encompasses not only deterministic maximal-in-range mechanisms, but also all universally-truthful randomized maximal in range algorithms, as well as a class of strictly more powerful truthful-in-expectation randomized mechanisms recently introduced by Dobzinski and Dughmi. Our result applies to any class of valuation functions that satisfies some minimal closure properties. These properties are satisfied by the valuation functions in all well-studied APX-hard social welfare maximization problems, such as coverage, submodular, and subadditive valuations. We also prove a stronger result for universally-truthful maximal-in-range mechanisms. Namely, even for the class of budgeted additive valuations, which admits an FPTAS, no such mechanism can achieve an approximation factor better than 1/k in polynomial time.