Strongly Polynomial-Time Truthful Mechanisms in One Shot

One of the main challenges in algorithmic mechanism design is to turn (existing) efficient algorithmic solutions into efficient truthful mechanisms. Building a truthful mechanism is indeed a difficult process since the underlying algorithm must obey certain “monotonicity” properties and suitable payment functions need to be computed (this task usually represents the bottleneck in the overall time complexity). We provide a general technique for building truthful mechanisms that provide optimal solutions in strongly polynomial time. We show that the entire mechanism can be obtained if one is able to express/write a strongly polynomial-time algorithm (for the corresponding optimization problem) as a “suitable combination” of simpler algorithms. This approach applies to a wide class of mechanism design graph problems, where each selfish agent corresponds to a weighted edge in a graph (the weight of the edge is the cost of using that edge). Our technique can be applied to several optimization problems which prior results cannot handle (e.g., MIN-MAX optimization problems). As an application, we design the first (strongly polynomial-time) truthful mechanism for the minimum diameter spanning tree problem, by obtaining it directly from an existing algorithm for solving this problem. For this non-utilitarian MIN-MAX problem, no truthful mechanism was known, even considering those running in exponential time (indeed, exact algorithms do not necessarily yield truthful mechanisms). Also, standard techniques for payment computations may result in a running time which is not polynomial in the size of the input graph. The overall Work partially supported by the Research Project GRID.IT, funded by the Italian Ministry of Education, University and Research, by the European Project IST-15964 “Algorithmic Principles for Building Efficient Overlay Computers” (AEOLUS), by the European Union under COST 295 (DYNAMO), and by the Swiss BBW. Part of this work has been developed while the first and the second author were visiting