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Unique bid auctions: Equilibrium solutions and experimental evidence

Author

Listed:
  • Rapoport, Amnon
  • Otsubo, Hironori
  • Kim, Bora
  • Stein, William E.

Abstract

Two types of auction were introduced on the Internet a few years ago and have rapidly been gaining widespread popularity. In both auctions, players compete for an exogenously determined prize by independently choosing an integer in some finite and common strategy space specified by the auctioneer. In the unique lowest (highest) bid auction, the winner of the prize is the player who submits the lowest (highest) bid, provided that it is unique. We construct the symmetric mixed-strategy equilibrium solutions to the two auctions, and then test them in a sequence of experiments that vary the number of bidders and size of the strategy space. Our results show that the aggregate bids, but only a minority of the individual bidders, are accounted for quite accurately by the equilibrium solutions.

Suggested Citation

  • Rapoport, Amnon & Otsubo, Hironori & Kim, Bora & Stein, William E., 2007. "Unique bid auctions: Equilibrium solutions and experimental evidence," MPRA Paper 4185, University Library of Munich, Germany, revised 17 Jul 2007.
    • Handle: RePEc:pra:mprapa:4185
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    References listed on IDEAS

    as
    1. Patrick Bajari & Ali Hortaçsu, 2004. "Economic Insights from Internet Auctions," Journal of Economic Literature, American Economic Association, vol. 42(2), pages 457-486, June.
    2. Rapoport, Amnon & Seale, Darryl A. & Winter, Eyal, 2002. "Coordination and Learning Behavior in Large Groups with Asymmetric Players," Games and Economic Behavior, Elsevier, vol. 39(1), pages 111-136, April.
    3. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    4. Rapoport, Amnon & Stein, William E. & Parco, James E. & Seale, Darryl A., 2004. "Equilibrium play in single-server queues with endogenously determined arrival times," Journal of Economic Behavior & Organization, Elsevier, vol. 55(1), pages 67-91, September.
    5. Raviv, Yaron & Virag, Gabor, 2009. "Gambling by auctions," International Journal of Industrial Organization, Elsevier, vol. 27(3), pages 369-378, May.
    6. Dov Monderer & Moshe Tennenholtz, 2004. "K-price auctions: Revenue inequalities, utility equivalence, and competition in auction design," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(2), pages 255-270, August.
    7. Ivanova-Stenzel, Radosveta & Sonsino, Doron, 2004. "Comparative study of one-bid versus two-bid auctions," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 561-583, August.
    8. Darryl A. Seale & Amnon Rapoport, 2000. "Elicitation of Strategy Profiles in Large Group Coordination Games," Experimental Economics, Springer;Economic Science Association, vol. 3(2), pages 153-179, October.
    9. Axel Ockenfels & David Reiley & Abdolkarim Sadrieh, 2006. "Online Auctions," NBER Working Papers 12785, National Bureau of Economic Research, Inc.
    10. Uri Gneezy, 2005. "Step-Level Reasoning and Bidding in Auctions," Management Science, INFORMS, vol. 51(11), pages 1633-1642, November.
    11. Theodore Turocy & Elizabeth Watson & Raymond Battalio, 2007. "Framing the first-price auction," Experimental Economics, Springer;Economic Science Association, vol. 10(1), pages 37-51, March.
    12. Darryl Seale & Amnon Rapoport, 2000. "Elicitation of Strategy Profiles in Large Group Coordination Games," Experimental Economics, Springer;Economic Science Association, vol. 3(2), pages 153-179, October.
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    Cited by:

    1. Raviv, Yaron & Virag, Gabor, 2009. "Gambling by auctions," International Journal of Industrial Organization, Elsevier, vol. 27(3), pages 369-378, May.
    2. Harold Houba & Dinard van der Laan & Dirk Veldhuizen, 2008. "The Unique-lowest Sealed-bid Auction," Tinbergen Institute Discussion Papers 08-049/1, Tinbergen Institute.
    3. Eichberger, Jürgen & Vinogradov, Dmitri, 2016. "Efficiency of Lowest-Unmatched Price Auctions," Economics Letters, Elsevier, vol. 141(C), pages 98-102.
    4. Yamada, Takashi & Hanaki, Nobuyuki, 2016. "An experiment on Lowest Unique Integer Games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 88-102.
    5. Cancan Zhou & Hongguang Dong & Rui Hu & Qinghua Chen, 2015. "Smarter than Others? Conjectures in Lowest Unique Bid Auctions," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-13, April.
    6. Harold Houba & Dinard Laan & Dirk Veldhuizen, 2011. "Endogenous entry in lowest-unique sealed-bid auctions," Theory and Decision, Springer, vol. 71(2), pages 269-295, August.
    7. Andrea Gallice, 2008. "Lowest Unique Bid Auctions over the Internet: Ability, Lottery or Scam?," Department of Economic Policy, Finance and Development (DEPFID) University of Siena 0608, Department of Economic Policy, Finance and Development (DEPFID), University of Siena.
    8. Rui Hu & Jinzhong Guo & Qinghua Chen & Tao Zheng, 2017. "The Psychological Force Model for Lowest Unique Bid Auction," Computational Economics, Springer;Society for Computational Economics, vol. 50(4), pages 655-667, December.
    9. Nadir Altinok & Abdurrahman Aydemir, 2015. "The Unfolding of Gender Gap in Education," Working Papers 934, Economic Research Forum, revised Aug 2015.
    10. Toomas Hinnosaar, 2013. "Penny Auctions are Unpredictable," Carlo Alberto Notebooks 305, Collegio Carlo Alberto.

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    More about this item

    Keywords

    unique bid auctions; equilibrium analysis; experiment;
    All these keywords.

    JEL classification:

    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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