Abstract
We consider randomized mechanisms for multi-dimensional scheduling. Following Lavi and Swamy [10], we study a setting with restrictions on the domain, while still preserving multi-dimensionality. In a sense, our setting is the simplest multi-dimensional setting, where each machine holds privately only a single-bit of information.
We prove a separation between truthful-in-expectation and universally truthful mechanisms for makespan minimization: We first show how to design an optimal truthful-in-expectation mechanism, and then prove lower bounds on the approximation guarantee of universally truthful mechanisms.
Research partially supported by the PRIN 2008 research project COGENT (COmputational and GamE-theoretic aspects of uncoordinated NeTworks), funded by the Italian Ministry of University and Research.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Archer, A., Tardos, E.: Truthful Mechanisms for One-Parameter Agents. In: Proc. 42nd FOCS, pp. 482–491 (2001)
Ashlagi, I., Dobzinski, S., Lavi, R.: An Optimal Lower Bound for Anonymous Scheduling Mechanisms. In: Proc. 10th EC, pp. 169–176 (2009)
Clarke, E.H.: Multipart pricing of public goods. Public Choice 11(1), 17–33 (1971)
Christodoulou, G., Koutsoupias, E., Kovács, A.: Mechanism design for fractional scheduling on unrelated machines. ACM Trans. on Algorithms 6(2) (2010)
Christodoulou, G., Koutsoupias, E., Vidali, A.: A Lower Bound for Scheduling Mechanisms. Algorithmica 55(4), 729–740 (2009)
Christodoulou, G., Kovács, A.: A deterministic truthful PTAS for scheduling related machines. In: Proc. of 21st SODA, pp. 1005–1016 (2010)
Dhangwatnotai, P., Dobzinski, S., Dughmi, S., Roughgarden, T.: Truthful Approximation Schemes for Single-Parameter Agents. SIAM J. on Computing 40(3), 915–933 (2011)
Groves, T.: Incentives in teams. Econometrica 41(4), 617–631 (1973)
Koutsoupias, E., Vidali, A.: A Lower Bound of 1 + φ for Truthful Scheduling Mechanisms. In: Kučera, L., Kučera, A. (eds.) MFCS 2007. LNCS, vol. 4708, pp. 454–464. Springer, Heidelberg (2007)
Lavi, R., Swamy, C.: Truthful mechanism design for multidimensional scheduling via cycle monotonicity. Games and Economic Behavior 67(1), 99–124 (2009)
Lu, P.: On 2-Player Randomized Mechanisms for Scheduling. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 30–41. Springer, Heidelberg (2009)
Lu, P., Yu, C.: An Improved Randomized Truthful Mechanism for Scheduling Unrelated Machines. In: Proc. of 25th STACS. LIPIcs, vol. 1, pp. 527–538 (2008)
Lu, P., Yu, C.: Randomized Truthful Mechanisms for Scheduling Unrelated Machines. In: Papadimitriou, C., Zhang, S. (eds.) WINE 2008. LNCS, vol. 5385, pp. 402–413. Springer, Heidelberg (2008)
Mu’alem, A., Schapira, M.: Setting Lower Bounds on Truthfulness. In: Proc. of 18th SODA, pp. 1143–1152 (2007)
Nisan, N., Ronen, A.: Algorithmic Mechanism Design. Games and Economic Behavior 35, 166–196 (2001)
Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.: Algorithmic Game Theory. Cambridge University Press (2007)
Vickrey, V.: Counterspeculations, auctions and competitive sealed tenders. Journal of Finance 16, 8–37 (1961)
Yu, C.: Truthful mechanisms for two-range-values variant of unrelated scheduling. Theoretical Computer Science 410(21-23), 2196–2206 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Auletta, V., Christodoulou, G., Penna, P. (2012). Mechanisms for Scheduling with Single-Bit Private Values. In: Serna, M. (eds) Algorithmic Game Theory. SAGT 2012. Lecture Notes in Computer Science, vol 7615. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33996-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-33996-7_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33995-0
Online ISBN: 978-3-642-33996-7
eBook Packages: Computer ScienceComputer Science (R0)