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Truthful mechanism design for multidimensional scheduling via cycle monotonicity

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  • Lavi, Ron
  • Swamy, Chaitanya

Abstract

We consider the makespan-minimization problem on unrelated machines in the context of algorithmic mechanism design. No truthful mechanisms with non-trivial approximation guarantees are known for this multidimensional domain. We study a well-motivated special case (also a multidimensional domain), where the processing time of a job on each machine is either "low" or "high." We give a general technique to convert any c-approximation algorithm (in a black-box fashion) to a 3c-approximation truthful-in-expectation mechanism. Our construction uses fractional truthful mechanisms as a building block, and builds upon a technique of Lavi and Swamy [Lavi, R., Swamy, C., 2005. Truthful and near-optimal mechanism design via linear programming. In: Proc. 46th FOCS, pp. 595-604]. When all jobs have identical low and high values, we devise a deterministic 2-approximation truthful mechanism. The chief novelty of our results is that we do not utilize explicit price definitions to prove truthfulness. Instead we design algorithms that satisfy cycle monotonicity [Rochet, J., 1987. A necessary and sufficient condition for rationalizability in a quasilinear context. J. Math. Econ. 16, 191-200], a necessary and sufficient condition for truthfulness in multidimensional settings; this is the first work that leverages this characterization.

Suggested Citation

  • Lavi, Ron & Swamy, Chaitanya, 2009. "Truthful mechanism design for multidimensional scheduling via cycle monotonicity," Games and Economic Behavior, Elsevier, vol. 67(1), pages 99-124, September.
  • Handle: RePEc:eee:gamebe:v:67:y:2009:i:1:p:99-124
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    References listed on IDEAS

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    1. Nisan, Noam & Ronen, Amir, 2001. "Algorithmic Mechanism Design," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 166-196, April.
    2. Sushil Bikhchandani & Shurojit Chatterji & Ron Lavi & Ahuva Mu'alem & Noam Nisan & Arunava Sen, 2006. "Weak Monotonicity Characterizes Deterministic Dominant-Strategy Implementation," Econometrica, Econometric Society, vol. 74(4), pages 1109-1132, July.
    3. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
    4. Gui Hongwei & Müller Rudolf & Vohra Rakesh, 2004. "Dominant Strategy Mechanisms with Multidimensional Types," Research Memorandum 047, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    5. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-631, July.
    6. McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
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    Cited by:

    1. Penna, Paolo & Ventre, Carmine, 2014. "Optimal collusion-resistant mechanisms with verification," Games and Economic Behavior, Elsevier, vol. 86(C), pages 491-509.
    2. Emerson Melo, 2018. "A Variational Approach to Network Games," Working Papers 2018.05, Fondazione Eni Enrico Mattei.
    3. Debasis Mishra & Anup Pramanik & Souvik Roy, 2013. "Implementation in multidimensional domains with ordinal restrictions," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 13-07, Indian Statistical Institute, New Delhi, India.

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