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Implementation in multidimensional dichotomous domains

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  • Debasis Mishra

    ()
    (Indian Statistical Institute, New Delhi)

  • Souvik Roy

    ()
    (University of Caen)

Abstract

We consider deterministic dominant strategy implementation in multidimensional dichotomous domains in private values and quasi-linear utility setting. In such multidimensional domains, an agent's type is characterized by a single number, the value of the agent, and a non-empty subset of acceptable alternatives. Each acceptable alternative gives the agent utility equal to his value and other alternatives give him zero utility. We show that generation monotonicity is necessary and sufficient for implementability in any dichotomous domain. If such a domain satisfies a richness condition, then a weaker version of generation monotonicity, which we call 2-generation monotonicity (equivalent to 3-cycle monotonicity), is necessary and sufficient for implementation. We use this result to derive the optimal mechanism in a one-sided matching problem with agents having dichotomous types.

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Bibliographic Info

Paper provided by Indian Statistical Institute, New Delhi, India in its series Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers with number 11-15.

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Length: 41 pages
Date of creation: Sep 2011
Date of revision:
Handle: RePEc:ind:isipdp:11-15

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Keywords: dominant strategy implementation; cycle monotonicity; dichotomous preferences; generation monotonicity;

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References

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  1. Berger André & Müller Rudolf & Naeemi Seyed Hossein, 2010. "Path-Monotonicity and Incentive Compatibility," Research Memorandum 035, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
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  3. Heydenreich, Birgit & Müller, Rudolf & Uetz, Marc & Vohra, Rakesh, 2008. "Characterization of Revenue Equivalence," Research Memorandum 001, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  4. Kos, Nenad & Messner, Matthias, 2013. "Extremal incentive compatible transfers," Journal of Economic Theory, Elsevier, vol. 148(1), pages 134-164.
  5. Juan Carlos Carbajal & Jeffrey C. Ely, 2012. "Mechanism Design Without Revenue Equivalence," Discussion Papers Series 458, School of Economics, University of Queensland, Australia.
  6. Marc Vorsatz, 2004. "Approval Voting ion Dichotomous Preferences," UFAE and IAE Working Papers 619.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  7. 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.
  8. Debasis Mishra & Souvik Roy, 2011. "Implementation in multidimensional dichotomous domains," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 11-15, Indian Statistical Institute, New Delhi, India.
  9. Babaioff, Moshe & Feldman, Michal & Nisan, Noam & Winter, Eyal, 2012. "Combinatorial agency," Journal of Economic Theory, Elsevier, vol. 147(3), pages 999-1034.
  10. 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, 07.
  11. Blackorby, Charles & Dezsö Szalay, 2007. "Multidimensional Screening, Affiliation, and Full Separation," The Warwick Economics Research Paper Series (TWERPS) 802, University of Warwick, Department of Economics.
  12. Olszewski, Wojciech & Chung, Kim-Sau, 2007. "A non-differentiable approach to revenue equivalence," Theoretical Economics, Econometric Society, vol. 2(4), December.
  13. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
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  15. 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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Citations

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Cited by:
  1. Debasis Mishra & Abdul Quadir, 2012. "Deterministic single object auctions with private values," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 12-06, Indian Statistical Institute, New Delhi, India.
  2. 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.
  3. Rahul Deb & Debasis Mishra, 2013. "Implementation with Securities," Working Papers tecipa-484, University of Toronto, Department of Economics.
  4. Debasis Mishra & Souvik Roy, 2011. "Implementation in multidimensional dichotomous domains," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 11-15, Indian Statistical Institute, New Delhi, India.
  5. Kos, Nenad & Messner, Matthias, 2013. "Incentive compatibility in non-quasilinear environments," Economics Letters, Elsevier, vol. 121(1), pages 12-14.
  6. Carbajal, Juan Carlos & McLennan, Andrew & Tourky, Rabee, 2013. "Truthful implementation and preference aggregation in restricted domains," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1074-1101.

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