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Implementation in multidimensional dichotomous domains

Author

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  • Mishra, Debasis

    () (Economics and Planning Unit, Indian Statistical Institute)

  • Roy, Souvik

    () (Economics and Planning Unit, Indian Statistical Institute)

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 set of acceptable alternatives. Each acceptable alternative gives the agent utility equal to his value and other alternatives give him zero utility. We identity a new condition, which we call generation monotonicity, that 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.

Suggested Citation

  • Mishra, Debasis & Roy, Souvik, 2013. "Implementation in multidimensional dichotomous domains," Theoretical Economics, Econometric Society, vol. 8(2), May.
  • Handle: RePEc:the:publsh:1239
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    Citations

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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. Kos, Nenad & Messner, Matthias, 2013. "Incentive compatibility in non-quasilinear environments," Economics Letters, Elsevier, vol. 121(1), pages 12-14.
    3. Rahul Deb & Debasis Mishra, 2014. "Implementation With Contingent Contracts," Econometrica, Econometric Society, vol. 82, pages 2371-2393, November.
    4. Mishra, Debasis & Pramanik, Anup & Roy, Souvik, 2016. "Local incentive compatibility with transfers," Games and Economic Behavior, Elsevier, vol. 100(C), pages 149-165.
    5. Ryuji Sano, 2016. "Iterative Revelation Mechanisms," KIER Working Papers 937, Kyoto University, Institute of Economic Research.
    6. Mishra, Debasis & Pramanik, Anup & Roy, Souvik, 2014. "Multidimensional mechanism design in single peaked type spaces," Journal of Economic Theory, Elsevier, vol. 153(C), pages 103-116.
    7. Mishra, Debasis & Roy, Souvik, 2013. "Implementation in multidimensional dichotomous domains," Theoretical Economics, Econometric Society, vol. 8(2), May.
    8. 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.
    9. 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.
    10. 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.
    11. Tomoya Kazumura & Debasis Mishra & Shigehiro Serizawa, 2017. "Mechanism design without quasilinearity," ISER Discussion Paper 1005, Institute of Social and Economic Research, Osaka University.

    More about this item

    Keywords

    Dominant strategy implementation; cycle monotonicity; dichotomous preferences; generation monotonicity;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D02 - Microeconomics - - General - - - Institutions: Design, Formation, Operations, and Impact
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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