We show that every universally truthful randomized mechanism for combinatorial auctions with submodular valuations that provides an approximation ratio of m 1 2 − must use exponentially many value queries, where m is the number of items. In contrast, ignoring incentives there exist constant ratio approximation algorithms for this problem. Our approach is based on a novel direct hardness technique that completely skips the notoriously hard step of characterizing truthful mechanisms. The characterization step was the main obstacle for proving impossibility results in algorithmic mechanism design so far. We demonstrate two additional applications of our new technique: (1) an impossibility result for universally-truthful polynomial time flexible combinatorial public projects and (2) an impossibility result for truthful-in-expectation mechanisms for exact combinatorial public projects. The latter is the first result that bounds the power of polynomial-time truthful in expectation mechanisms in any setting.
REF proved that every universally truthful randomized mechanism for CAs with submodular valuations with an approximation ratio of m 1/2−ε , for some ε > 0, must use exponentially many value oracles.
An impossibility result for truthful combinatorial auctions with submodular valuations
STOC '11
Mathematics Computer Science