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A universally-truthful approximation scheme for multi-unit auctions

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  • Vöcking, Berthold

Abstract

We present a randomized incentive-compatible polynomial-time approximation scheme for multi-unit auctions. For every fixed ϵ>0, the approximation scheme provides a polynomial-time algorithm approximating the optimal social welfare within a factor of 1−ϵ. Our mechanism is truthful in the universal sense, i.e., it is a distribution over deterministically truthful mechanisms. It employs VCG payments in a non-standard way as the underlying deterministic mechanisms are not maximal in range and do not belong to the class of affine maximizers. Instead, each of them is composed of a collection of affine maximizers, one for each bidder. This yields a subjective variant of VCG in which payments for different bidders are defined on the basis of possibly different affine maximizers.

Suggested Citation

  • Vöcking, Berthold, 2019. "A universally-truthful approximation scheme for multi-unit auctions," Games and Economic Behavior, Elsevier, vol. 113(C), pages 4-16.
    • Handle: RePEc:eee:gamebe:v:113:y:2019:i:c:p:4-16
    DOI: 10.1016/j.geb.2013.12.007
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    References listed on IDEAS

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    1. Mu'alem, Ahuva & Nisan, Noam, 2008. "Truthful approximation mechanisms for restricted combinatorial auctions," Games and Economic Behavior, Elsevier, vol. 64(2), pages 612-631, November.
    2. 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.
    3. G. L. Nemhauser & Z. Ullmann, 1969. "Discrete Dynamic Programming and Capital Allocation," Management Science, INFORMS, vol. 15(9), pages 494-505, May.
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    More about this item

    Keywords

    Mechanism design; Multi-unit auctions; Universal truthfulness;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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