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Optimal Mechanisms for Single Machine Scheduling


  • Heydenreich Birgit
  • Mishra Debasis
  • Müller Rudolf
  • Uetz Marc



We study the design of optimal mechanisms in a setting where job-agents compete for being processed by a service provider that can handle one job at a time. Each job has a processing time and incurs a waiting cost. Jobs need to be compensated for waiting. We consider two models, one where only the waiting costs of jobs are private information (1-d), and another where both waiting costs and processing times are private (2-d). Probability distributions represent the public common belief about private information. We consider discrete and continuous distributions. In this setting, an optimal mechanism minimizes the total expected expenses to compensate all jobs, while it has to be Bayes-Nash incentive compatible. We derive closed formulae for the optimal mechanism in the 1-d case and show that it is efficient for symmetric jobs. For non-symmetric jobs, we show that efficient mechanisms perform arbitrarily bad. For the 2-d discrete case, we prove that the optimal mechanism in general does not even satisfy IIA, the `independent of irrelevant alternatives'' condition. Hence any attempt along the lines of the classical auction setting is doomed to fail. In the 2-d discrete case, we also show that the optimal mechanism is not even efficient for symmetric agents.

Suggested Citation

  • Heydenreich Birgit & Mishra Debasis & Müller Rudolf & Uetz Marc, 2008. "Optimal Mechanisms for Single Machine Scheduling," Research Memorandum 033, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  • Handle: RePEc:unm:umamet:2008033

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    References listed on IDEAS

    1. Birgit Heydenreich & Rudolf Müller & Marc Uetz & Rakesh V. Vohra, 2009. "Characterization of Revenue Equivalence," Econometrica, Econometric Society, vol. 77(1), pages 307-316, January.
    2. Muller, Rudolf & Perea, Andres & Wolf, Sascha, 2007. "Weak monotonicity and Bayes-Nash incentive compatibility," Games and Economic Behavior, Elsevier, vol. 61(2), pages 344-358, November.
    3. Manipushpak Mitra, 2001. "Mechanism design in queueing problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 17(2), pages 277-305.
    4. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    5. Mark Armstrong, 2000. "Optimal Multi-Object Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 455-481.
    6. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    7. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
    8. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-631, July.
    9. Rochet, Jean-Charles, 1987. "A necessary and sufficient condition for rationalizability in a quasi-linear context," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 191-200, April.
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