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An approximation algorithm for multi-unit auctions: numerical and subject experiments

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  • Satoshi Takahashi
  • Yoichi Izunaga
  • Naoki Watanabe

Abstract

In multi-unit auctions for a single item, the Vickrey–Clarke–Groves mechanism (VCG) attains allocative efficiency but suffers from its computational complexity. Takahashi and Shigeno thus proposed a greedy based approximation algorithm (GBA). In a subject experiment there was truly a difference in efficiency rate but no significant difference in seller’s revenue between GBA and VCG. It is not clear in theory whether each bidder will submit his or her true unit valuations in GBA. We show, however, that in a subject experiment there was no significant difference in the number of bids that obey “almost” truth-telling between GBA and VCG. As for individual bidding behavior, GBA and VCG show a sharp contrast when a human bidder competes against machine bidders; underbidding was observed in GBA, while overbidding was observed in VCG. Some results in a numerical experiment are also provided prior to reporting those observations.

Suggested Citation

  • Satoshi Takahashi & Yoichi Izunaga & Naoki Watanabe, 2018. "An approximation algorithm for multi-unit auctions: numerical and subject experiments," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 28(1), pages 95-115.
    • Handle: RePEc:wut:journl:v:1:y:2018:p:95-115:id:1351
    DOI: 10.5277/ord180105
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    References listed on IDEAS

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    1. Chen, Yan & Takeuchi, Kan, 2010. "Multi-object auctions with package bidding: An experimental comparison of Vickrey and iBEA," Games and Economic Behavior, Elsevier, vol. 68(2), pages 557-579, March.
    2. Kagel, John H & Levin, Dan, 2001. "Behavior in Multi-unit Demand Auctions: Experiments with Uniform Price and Dynamic Vickrey Auctions," Econometrica, Econometric Society, vol. 69(2), pages 413-454, March.
    3. John H. Kagel & Alvin E. Roth, 2016. "The Handbook of Experimental Economics, Volume 2," Economics Books, Princeton University Press, edition 1, volume 2, number 10874.
    4. Dobzinski, Shahar & Nisan, Noam, 2015. "Multi-unit auctions: Beyond Roberts," Journal of Economic Theory, Elsevier, vol. 156(C), pages 14-44.
    5. Lawrence M. Ausubel, 2004. "An Efficient Ascending-Bid Auction for Multiple Objects," American Economic Review, American Economic Association, vol. 94(5), pages 1452-1475, December.
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    1. Satoshi Takahashi & Yoichi Izunaga & Naoki Watanabe, 2019. "VCG mechanism for multi-unit auctions and appearance of information: a subject experiment," Evolutionary and Institutional Economics Review, Springer, vol. 16(2), pages 357-374, December.
    2. Satoshi Takahashi & Yoichi Izunaga & Naoki Watanabe, 2022. "An experimental study of VCG mechanism for multi-unit auctions: competing with machine bidders," Evolutionary and Institutional Economics Review, Springer, vol. 19(1), pages 97-117, April.

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