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Implementation in multidimensional dichotomous domains

Author

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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.

Suggested Citation

  • Debasis Mishra & Souvik Roy, 2011. "Implementation in multidimensional dichotomous domains," Discussion Papers 11-15, Indian Statistical Institute, Delhi.
    • Handle: RePEc:alo:isipdp:11-15
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    Cited by:

    1. 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.
    2. Rahul Deb & Debasis Mishra, 2014. "Implementation With Contingent Contracts," Econometrica, Econometric Society, vol. 82, pages 2371-2393, November.
    3. Kazumura, Tomoya & Mishra, Debasis & Serizawa, Shigehiro, 2020. "Mechanism design without quasilinearity," Theoretical Economics, Econometric Society, vol. 15(2), May.
    4. Ryuji Sano, 2021. "Dynamic communication mechanism design," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 163-180, July.
    5. 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.
    6. Kos, Nenad & Messner, Matthias, 2013. "Incentive compatibility in non-quasilinear environments," Economics Letters, Elsevier, vol. 121(1), pages 12-14.
    7. Mishra, Debasis & Pramanik, Anup & Roy, Souvik, 2016. "Local incentive compatibility with transfers," Games and Economic Behavior, Elsevier, vol. 100(C), pages 149-165.
    8. Sano, Ryuji, 2021. "Dynamic slot allocations with different patience levels," Games and Economic Behavior, Elsevier, vol. 130(C), pages 465-473.
    9. Debasis Mishra & Anup Pramanik & Souvik Roy, 2013. "Implementation in multidimensional domains with ordinal restrictions," Discussion Papers 13-07, Indian Statistical Institute, Delhi.
    10. De, Parikshit & Mitra, Manipushpak, 2019. "Balanced implementability of sequencing rules," Games and Economic Behavior, Elsevier, vol. 118(C), pages 342-353.
    11. Rahul Deb & Debasis Mishra, 2013. "Implementation with Securities," Working Papers tecipa-484, University of Toronto, Department of Economics.
    12. Ryuji Sano, 2016. "Iterative Revelation Mechanisms," KIER Working Papers 937, Kyoto University, Institute of Economic Research.
    13. Nicolò, Antonio & Sen, Arunava & Yadav, Sonal, 2019. "Matching with partners and projects," Journal of Economic Theory, Elsevier, vol. 184(C).

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    More about this item

    Keywords

    dominant strategy implementation; cycle monotonicity; dichotomous preferences; generation monotonicity;
    All these keywords.

    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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