Setting lower bounds on truthfulness

This paper presents inapproximability results for paradigmatic multi-dimensional truthful mechanism design problems. We first show a lower bound of 2−[Formula presented] for the scheduling problem with n unrelated machines (formulated as a mechanism design problem in the seminal paper of Nisan and Ronen on Algorithmic Mechanism Design). Our lower bound applies to universally-truthful randomized mechanisms, regardless of any computational assumptions on the running time of these mechanisms. Moreover, it holds even for the wider class of truthfulness-in-expectation mechanisms. We then turn to Bayesian settings and show a lower bound of 1.2 for Bayesian Incentive-Compatible (BIC) mechanisms. No lower bounds for truthful mechanisms in multi-dimensional settings which incorporate randomness were previously known. Next, we define the workload-minimization problem in networks. We prove lower bounds for the inter-domain routing setting presented by Feigenbaum, Papadimitriou, Sami, and Shenker. Finally, we prove lower bounds for Max–Min fairness, Min–Max fairness, and envy minimization.