The Power of Verification for One-Parameter Agents
We study combinatorial optimization problems involving one-parameter selfish agents considered by Archer and Tardos [FOCS 2001]. In particular, we show that, if agents can lie in one direction (that is they either overbid or underbid) then any (polynomial-time) c-approximation algorithm, for the optimization problem without selfish agents, can be turned into a (polynomial-time) c(1+ε)-approximation truthful mechanism, for any ε >0. We then look at the Q||C max problem in the case of agents owning machines of different speeds. We consider the model in which payments are given to the agents only after the machines have completed the jobs assigned. This means that for each machine that receives at least one job, the mechanism can verify if the corresponding agent declared a greater speed. For this setting, we characterize the allocation algorithms A that admit a payment function P such that M=(A,P) is a truthful mechanism. In addition, we give a (1+ε)-approximation truthful mechanism for Q||C max when machine speeds are bounded by a constant. Finally, we consider the classical scheduling problem Q|| ∑ w j C j which does not admit an exact mechanism if verification is not allowed. By contrast, we show that an exact mechanism for Q|| ∑ w j C j exists when verification is allowed.
KeywordsCombinatorial Optimization Problem Allocation Algorithm Positive Load Adjustment Phase Weakly Monotone
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- 1.Archer, A., Tardos, E.: Truthful mechanisms for one-parameter agents. In: Proc. of the IEEE Symposium on Foundations of Computer Science, pp. 482–491 (2001)Google Scholar
- 2.Auletta, V., De Prisco, R., Penna, P., Persiano, G.: Deterministic truthful approximation mechanisms for scheduling related machines. Technical report, To appear in Proceedings of STACS 2004 (2004)Google Scholar
- 3.Auletta, V., De Prisco, R., Penna, P., Persiano, G.: How to tax and route selfish unsplittable traffic. Technical report, To appear in Proceedings of SPAA (2004)Google Scholar
- 5.Clarke, E.H.: Multipart Pricing of Public Goods. Public Choice, 17–33 (1971)Google Scholar
- 8.Nisan, N., Ronen, A.: Algorithmic Mechanism Design. In: Proc. of the 31st Annual ACM Symposium on Theory of Computing, pp. 129–140 (1999)Google Scholar
- 9.Vickrey, W.: Counterspeculation, Auctions and Competitive Sealed Tenders. Journal of Finance, 8–37 (1961)Google Scholar