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Incentives and justice for sequencing problems

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Abstract

We address the mechanism design issue for the sequencing problem. We identify the just sequencing rule that serves the agents in the non-increasing order of their waiting costs and prove that it is a Rawlsian rule and that it weakly lexi-max cost dominates the outcome efficient sequencing rule. We identify all ICJ mechanisms that implement the just sequencing rule. The other properties of the just sequencing rule that we identify are the following. It can be implemented with budget-balanced ICJ mechanisms. When waiting cost and processing time are private information, we identify all generalized ICJ mechanisms that ex-post implement the just sequencing rule. Finally, we identify all budget-balanced generalized ICJ mechanisms.

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Notes

  1. See Theorem 5.9. in Nisan and Ronen (2001).

  2. In our problem, we have a single machine implying that the make-span time is fixed throughout.

  3. See Theorem 5.5 in Nisan and Ronen (2001).

  4. Ex-post implementability literature includes contributions of Bergemann and Morris (2008), Bikhchandani (2006), Chung and Ely (2003), Jehiel et al. (2006), Jehiel and Moldovanu (2001), and Fieseler et al. (2003)). For the sequencing problem with private information only in processing time, incentive issues were addressed by Hain and Mitra (2004) and Moulin (2007).

  5. The sequencing rule is a function and not a correspondence. Hence, we will require tie-breaking rule to reduce a correspondence to a function. For reasons to be clarified later, we will use different tie-breaking rules for different sequencing rules.

  6. Mitra (2002) and Suijs (1996).

  7. A similar argument for the pivotal-based representation of VCG transfers [like condition (2)] for the queueing problem can be found in Chun et al. (2014).

  8. If there are more than one agent for whom the cost is the maximum, pick any one of them arbitrarily.

  9. If \(s_1=s_n\), then we have the queueing problem.

  10. See equation (3.1) in Mitra (2002).

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Authors and Affiliations

  1. Economic Research Unit, Indian Statistical Institute, Kolkata, 700108, India

    Parikshit De & Manipushpak Mitra

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  1. Parikshit De
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  2. Manipushpak Mitra
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Correspondence to Manipushpak Mitra.

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The authors would like to thank Anuj Bhowmik, Satya R. Chakravarty, Debasis Mishra, Suresh Mutuswami, Arunava Sen, two anonymous referees and the Associate Editor for helpful comments and suggestions.

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De, P., Mitra, M. Incentives and justice for sequencing problems. Econ Theory 64, 239–264 (2017). https://doi.org/10.1007/s00199-016-0983-2

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