A Characterization of 2-Player Mechanisms for Scheduling

We study the mechanism design problem of scheduling unrelated machines and we completely characterize the decisive truthful mechanisms for two players when the domain contains both positive and negative values. We show that the class of truthful mechanisms is very limited: A decisive truthful mechanism partitions the tasks into groups so that the tasks in each group are allocated independently of the other groups. Tasks in a group of size at least two are allocated by an affine minimizer and tasks in singleton groups by a task-independent mechanism. This characterization is about all truthful mechanisms, including those with unbounded approximation ratio. A direct consequence of this approach is that the approximation ratio of mechanisms for two players is 2, even for two tasks. In fact, it follows that for two players, VCG is the unique algorithm with optimal approximation 2. This characterization provides some support that any decisive truthful mechanism (for 3 or more players) part...

• Type: Conference
• Year: 2008
• Where: ESA
• Authors: George Christodoulou, Elias Koutsoupias, Angelina Vidali
• Keywords: Algorithms, Decisive Truthful Mechanism, ESA 2008, Truthful Mechanism, Truthful Mechanism Partitions