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Truthful implementation and preference aggregation in restricted domains

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  • Carbajal, Juan Carlos
  • McLennan, Andrew
  • Tourky, Rabee

Abstract

In a setting where agents have quasi-linear utilities over social alternatives and a transferable commodity, we consider three properties that a social choice function may possess: truthful implementation (in dominant strategies); monotonicity in differences; and lexicographic affine maximization. We introduce the notion of a flexible domain of preferences that allows elevation of pairs and study which of these conditions implies which others in such domain. We provide a generalization of the theorem of Roberts (1979) [36] in restricted valuation domains. Flexibility holds (and the theorem is not vacuous) if the domain of valuation profiles is restricted to the space of continuous functions defined on a compact metric space, or the space of piecewise linear functions defined on an affine space, or the space of smooth functions defined on a compact differentiable manifold. We provide applications of our results to public goods allocation settings, with finite and infinite alternative sets.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jetheo:v:148:y:2013:i:3:p:1074-1101
    DOI: 10.1016/j.jet.2012.11.001
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Carbajal, Juan Carlos & Müller, Rudolf, 2015. "Implementability under monotonic transformations in differences," Journal of Economic Theory, Elsevier, vol. 160(C), pages 114-131.
    2. Kazuhiko Hashimoto & Kohei Shiozawa, 2016. "Strategy-Proof Probabilistic Mechanisms for Public Decision with Money," ISER Discussion Paper 0964, Institute of Social and Economic Research, Osaka University.
    3. Thierry Marchant & Debasis Mishra, 2015. "Mechanism design with two alternatives in quasi-linear environments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(2), pages 433-455, February.
    4. M. Yenmez, 2015. "Incentive compatible market design with applications," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(3), pages 543-569, August.
    5. 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.
    6. Dobzinski, Shahar & Nisan, Noam, 2015. "Multi-unit auctions: Beyond Roberts," Journal of Economic Theory, Elsevier, vol. 156(C), pages 14-44.
    7. Paul H. Edelman & John A Weymark, 2017. "Dominant Strategy Implementability, Zero Length Cycles, and Affine Maximizers," Vanderbilt University Department of Economics Working Papers 17-00002, Vanderbilt University Department of Economics.
    8. Fasil Alemante & Donald E. Campbell & Jerry S. Kelly, 2016. "Characterizing the resolute part of monotonic social choice correspondences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(4), pages 765-783, October.
    9. Yi, Jianxin & Li, Yong, 2016. "A general impossibility theorem and its application to individual rights," Mathematical Social Sciences, Elsevier, vol. 81(C), pages 79-86.
    10. Quadir, Abdul, 2017. "Spanning tree auctions: A complete characterization," Mathematical Social Sciences, Elsevier, vol. 86(C), pages 1-8.
    11. repec:spr:etbull:v:2:y:2014:i:1:d:10.1007_s40505-014-0031-y is not listed on IDEAS

    More about this item

    Keywords

    Robertsʼ theorem; Truthful implementation; Monotonicity in differences; Lexicographic affine maximization; Domain restrictions;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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