Efficient Truthful Scheduling and Resource Allocation through Monitoring

We study the power and limitations of the Vickrey-ClarkeGroves mechanism with monitoring (VCG) for cost minimization problems with objective functions that are more general than the social cost. We identify a simple and natural sufficient condition for VCG to be truthful for general objectives. As a consequence, we obtain that for any cost minimization problem with non-decreasing objective μ, VCG is truthful, if the allocation is Maximal-in-Range and μ is 1-Lipschitz (e.g., μ can be the Lp-norm of the agents’ costs, for any p ≥ 1 or p = ∞). We apply VCG to scheduling on restricted-related machines and obtain a polynomial-time truthful-in-expectation 2-approximate (resp. O(1)-approximate) mechanism for makespan (resp. Lp-norm) minimization. Moreover, applying VCG, we obtain polynomial-time truthful O(1)-approximate mechanisms for some fundamental bottleneck network optimization problems with single-parameter agents. On the negative side, we provide strong evidence that VCG could not lead to computationally efficient truthful mechanisms with reasonable approximation ratios for binary covering social cost minimization problems. However, we show that VCG results in computationally efficient approximately truthful mechanisms for binary covering problems.