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Implementation in multidimensional domains with ordinal restrictions

  • Debasis Mishra

    ()

    (Indian Statistical Institute, New Delhi)

  • Anup Pramanik

    (Indian Statistical Institute, New Delhi)

  • Souvik Roy

    (Indian Statistical Institute, New Delhi)

We consider implementation of a deterministic allocation rule using transfers in quasi-linear private values environments. We show that if the type space is a multidimensional domain satisfying some ordinal restrictions, then an allocation rule is implementable in such a domain if and only if it satisfies a familiar and simple condition called 2-cycle monotonicity. Our ordinal restrictions cover type spaces which are non-convex, e.g., the single peaked domain and its generalizations. We apply our result to show that in the single peaked domain, a local version of 2-cycle monotonicity is necessary and sufficient for implementation and every locally incentive compatible mechanism is incentive compatible.

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File URL: http://www.isid.ac.in/~pu/dispapers/dp13-07.pdf
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Paper provided by Indian Statistical Institute, New Delhi, India in its series Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers with number 13-07.

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Length: 32 pages
Date of creation: May 2013
Date of revision:
Handle: RePEc:ind:isipdp:13-07
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  1. John A. Weymark, 2008. "Strategy-Proofness and the Tops-Only Property," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(1), pages 7-26, 02.
  2. Nenad Kos & Matthias Messner, 2010. "Extremal Incentive Compatible Transfers," Working Papers 359, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  3. Katherine Cuff & Sunghoon Hong & Jesse Schwartz & Quan Wen & John Weymark, 2011. "Dominant Strategy Implementation with a Convex Product Space of Valuations," Vanderbilt University Department of Economics Working Papers 1104, Vanderbilt University Department of Economics.
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  11. Krishna, Vijay & Maenner, Eliot, 2001. "Convex Potentials with an Application to Mechanism Design," Econometrica, Econometric Society, vol. 69(4), pages 1113-19, July.
  12. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-19, March.
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  15. 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.
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