Mechanisms for Scheduling with Single-Bit Private Values

We study the problem of designing truthful mechanisms for makespan minimization in scheduling. In particular, we consider randomized mechanisms for a restriction of the general multi-dimensional domain (i.e., unrelated machines). In a sense, our setting is the simplest multi-dimensional setting, where each machine holds privately only a single-bit of information. Some of the impossibility results for deterministic mechanisms carry over our setting as well. We prove a separation between truthful-in-expectation and universally truthful mechanisms for makespan minimization: We first show how to design an optimal truthful-in-expectation mechanism, and then prove lower bounds on the approximation guarantee of universally truthful mechanisms.