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Implementation in multidimensional dichotomous domains

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    (Economics and Planning Unit, Indian Statistical Institute)

  • ,

    (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.

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  • , & ,, 2013. "Implementation in multidimensional dichotomous domains," Theoretical Economics, Econometric Society, vol. 8(2), May.
    • Handle: RePEc:the:publsh:1239
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    Cited by:

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    3. Ryuji Sano, 2016. "Iterative Revelation Mechanisms," KIER Working Papers 937, Kyoto University, Institute of Economic Research.
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    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.
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    10. 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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