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.
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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.
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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)
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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
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DOI: https://doi.org/10.1007/978-3-642-33996-7_3
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