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Robertsʼ Theorem with neutrality: A social welfare ordering approach

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  • Mishra, Debasis
  • Sen, Arunava

Abstract

We consider dominant strategy implementation in private values settings, when agents have multi-dimensional types, the set of alternatives is finite, monetary transfers are allowed, and agents have quasi-linear utilities. We focus on private-value environments. We show that any implementable and neutral social choice function must be a weighted welfare maximizer if the type space of every agent is an m-dimensional open interval, where m is the number of alternatives. When the type space of every agent is unrestricted, Robertsʼ Theorem with neutrality (Roberts, 1979) becomes a corollary to our result. Our proof technique uses a social welfare ordering approach, commonly used in aggregation literature in social choice theory. We also prove the general (affine maximizer) version of Robertsʼ Theorem for unrestricted type spaces of agents using this approach.

Suggested Citation

  • Mishra, Debasis & Sen, Arunava, 2012. "Robertsʼ Theorem with neutrality: A social welfare ordering approach," Games and Economic Behavior, Elsevier, vol. 75(1), pages 283-298.
  • Handle: RePEc:eee:gamebe:v:75:y:2012:i:1:p:283-298
    DOI: 10.1016/j.geb.2011.11.005
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    References listed on IDEAS

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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. 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. Dobzinski, Shahar & Nisan, Noam, 2015. "Multi-unit auctions: Beyond Roberts," Journal of Economic Theory, Elsevier, vol. 156(C), pages 14-44.
    4. 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.
    5. Quadir, Abdul, 2017. "Spanning tree auctions: A complete characterization," Mathematical Social Sciences, Elsevier, vol. 86(C), pages 1-8.
    6. 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.
    7. 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

    Dominant strategy mechanism design; Robertsʼ Theorem; Affine maximizers; Social welfare ordering;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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