| Summary: | We consider incentive compatible mechanisms for a domain that is very close to the domain of scheduling n unrelated machines: the single exception is that the valuation of just one machine is submodular. For the scheduling problem with such cost functions, we give a lower bound of Ω(√n) on the approximation ratio of incentive compatible deterministic mechanisms. This is a strong information-theoretic impossibility result on the approximation ratio of mechanisms that provides strong evidence for the Nisan-Ronen conjecture. This is the first non-constant lower bound that assumes no restriction on the mechanism side; in contrast, all previous general results hold for only special classes of mechanisms such as local, strongly monotone, and anonymous mechanisms. Our approach is based on a novel multi-player characterization of appropriately selected instances that allows us to focus on particular type of algorithms, linear mechanisms, and it is a potential stepping stone towards the full resolution of the conjecture.
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