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 running time of our mechanism, instead, is polynomial in the number n of nodes and m of edges, and it is only a factor O(nα(n,n)) away from the best known canonical centralized algorithm.
Unable to display preview. Download preview PDF.
- 2.Archer, A., Tardos, É.: Truthful mechanisms for one-parameter agents. In: Proc. of 42nd FOCS, pp. 482–491 (2001)Google Scholar
- 3.Clarke, E.H.: Multipart Pricing of Public Goods. Public Choice, 17–33 (1971)Google Scholar
- 9.Hershberger, J., Suri, S.: Vickrey prices and shortest paths: what is an edge worth? In: Proc. of the 42nd FOCS, pp. 252–259 (2001)Google Scholar
- 10.Kao, M.-Y., Li, X.-Y., Wang, W.: Towards truthful mechanisms for binary demand games: A general framework. In: Proc. of ACM EC, pp. 213–222 (2005)Google Scholar
- 12.Mu’Alem, A., Nisan, N.: Truthful approximation mechanisms for restricted combinatorial auctions. In: Proc. of 18th AAAI, pp. 379–384 (2002)Google Scholar
- 15.Nisan, N., Ronen, A.: Algorithmic mechanism design. In: Proc. of the 31st STOC, pp. 129–140 (1999)Google Scholar
- 16.Papadimitriou, C.H.: Algorithms, games, and the Internet. In: Proc. of the 33rd STOC, pp. 749–753 (2001)Google Scholar
- 17.Penna, P., Proietti, G., Widmayer, P.: Strongly polynomial-time truthful mechanisms in one shot. Technical report, Università di Salerno (2006), Available at: http://ec.tcfs.it/Group/Selfish_Agents.html
- 18.Pettie, S., Ramachandran, V.: Computing shortest paths with comparisons and additions. In: Proc. of the 13th SODA, pp. 267–276 (2002)Google Scholar
- 19.Proietti, G., Widmayer, P.: A truthful mechanism for the non-utilitarian minimum radius spanning tree problem. In: Proc. of SPAA, pp. 195–202 (2005)Google Scholar