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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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  1. Müller,Rudolf & Perea,Andrés & Wolf,Sascha, 2005. "Weak Monotonicity and Bayes-Nash Incentive Compatibility," Research Memorandum 039, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
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  6. Juan Carlos Carbajal & Jeffrey C. Ely, 2012. "Mechanism Design Without Revenue Equivalence," Discussion Papers Series 458, School of Economics, University of Queensland, Australia.
  7. Garud Iyengar & Anuj Kumar, 2008. "Optimal procurement mechanisms for divisible goods with capacitated suppliers," Review of Economic Design, Springer, vol. 12(2), pages 129-154, June.
  8. Olszewski, Wojciech & Chung, Kim-Sau, 2007. "A non-differentiable approach to revenue equivalence," Theoretical Economics, Econometric Society, vol. 2(4), December.
  9. Marc Vorsatz, 2007. "Approval Voting on Dichotomous Preferences," Social Choice and Welfare, Springer, vol. 28(1), pages 127-141, January.
  10. 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).
  11. 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.
  12. Babaioff, Moshe & Feldman, Michal & Nisan, Noam & Winter, Eyal, 2012. "Combinatorial agency," Journal of Economic Theory, Elsevier, vol. 147(3), pages 999-1034.
  13. 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.
  14. Mishra, Debasis & Roy, Souvik, 2013. "Implementation in multidimensional dichotomous domains," Theoretical Economics, Econometric Society, vol. 8(2), May.
  15. 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.
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Cited by:
  1. 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.
  2. Rahul Deb & Debasis Mishra, 2013. "Implementation with securities," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 13-05, Indian Statistical Institute, New Delhi, India.
  3. Mishra, Debasis & Roy, Souvik, 2013. "Implementation in multidimensional dichotomous domains," Theoretical Economics, Econometric Society, vol. 8(2), May.
  4. 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.
  5. Kos, Nenad & Messner, Matthias, 2013. "Incentive compatibility in non-quasilinear environments," Economics Letters, Elsevier, vol. 121(1), pages 12-14.
  6. 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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