Amplified Hardness of Approximation for VCG-Based Mechanisms

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, submodu...

• Type: Conference
• Year: 2010
• Where: SODA
• Authors: Shaddin Dughmi, Hu Fu, Robert Kleinberg
• Keywords: Discrete Algorithms, Social Welfare Maximization, SODA 2010, Two-player Hardness Assumption, Welfare Maximization Problem