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The Impact of Discrete Bidding and Bidder Aggressiveness on Sellers' Strategies in Open English Auctions: Reserves and Covert Shilling


  • Atanu R. Sinha

    () (College of Business, University of Colorado, Campus Box 419, Boulder, Colorado 80309-0419)

  • Eric A. Greenleaf

    () (The Stern School of Business, 44 West Fourth Street, New York University, New York, New York 10012)


In practice, the rules in most open English auctions require participants to raise bids by a sizeable, discrete amount. Furthermore, some bidders are typically more aggressive in seeking to become the “current bidder” during competitive bidding. Most auction theory, however, has assumed bidders can place any tiny “continuous” bid increase, and recommend as optimal the tiniest possible increase. This article examines how incorporating discrete bidding and bidder aggressiveness affect optimal strategies for an important decision for auction sellers, which is setting the lowest acceptable bid at which to sell the property. We investigate two alternative methods sellers often use to enforce this decision. These are setting an irrevocable before the auction, and , where the seller or confederates pose as bona fide bidders and raise bona fide bids, unsuspected by bidders. These optimal strategies interest auction participants, especially sellers who must recognize the bidding rules and bidder aggressiveness they will encounter in actual auctions. We also examine how these strategies change with the auction context, such as the number of bidders, and how they differ from corresponding strategies already identified for continuous bidding. Our model examines open English auctions where bidders have independent, private valuations. We find that discrete bidding does affect these strategies, as does the aggressiveness of the bidder with the highest valuation, to the average aggressiveness of all other remaining bidders. We identify the seller's optimal discrete reserve, and show that if the highest valuator is relatively more (less) aggressive, this increases (decreases) from the optimal continuous reserve, and also increases (decreases) as the number of bidders increases. With continuous bidding, by contrast, this reserve is invariant to the number of bidders. As this bidder becomes relatively more aggressive, for a given number of bidders, the optimal discrete reserve increases, while as he or she becomes less aggressive, the seller's expected auction utility increases, which increases the set of auctions where discrete bidding generates higher seller welfare than continuous. We propose a covert shilling model that requires shilling sellers, and any confederates and auctioneers, to outwardly act no differently than with reserves, to avoid detection. We identify cases where the seller optimally shills once the bona fide bidding has stopped, and identify the corresponding optimal point to stop shilling and accept the next bona fide bid, if offered. This stopping point does not depend on where bona fide bidding stops, or aggressiveness, or the number of bidders, or on whether shill bids alternate with bona fide bids or are consecutively entered. We also find that the optimal lowest acceptable bid with shilling can be higher (lower) than that with reserves if the highest valuator is sufficiently unaggressive (aggressive). By comparison, in continuous bidding shilling and reserves yield identical lowest acceptable bids. Sometimes the seller using a shilling strategy optimally should not shill at all, and instead accept the bid where bona fide bidding stops. This can occur when that bid, or the number of bidders, is sufficiently high, or when the highest valuator is as, or less, aggressive than other bidders. Optimal shilling can be as practical to implement as reserves, because it does not require sellers to have any information beyond that needed in a reserve auction. If sellers shill optimally, they can never be worse off compared to using a reserve, and can be better off. Shilling can make bidders worse off, but can also make them better off when the seller using a shilling strategy optimally accepts bids below the optimal reserve. In these latter cases, shilling Pareto dominates reserves, ex ante. We provide numerical examples to illustrate these results. We discuss how our results might be affected if shilling is not covert, or bidders' valuations have a common value component rather than being independent, or by the rules used in many discrete bid Internet auctions.

Suggested Citation

  • Atanu R. Sinha & Eric A. Greenleaf, 2000. "The Impact of Discrete Bidding and Bidder Aggressiveness on Sellers' Strategies in Open English Auctions: Reserves and Covert Shilling," Marketing Science, INFORMS, vol. 19(3), pages 244-265, May.
  • Handle: RePEc:inm:ormksc:v:19:y:2000:i:3:p:244-265

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    References listed on IDEAS

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    Cited by:

    1. Ricardo Gonçalves, 2008. "A communication equilibrium in English auctions with discrete bidding," Working Papers de Economia (Economics Working Papers) 042008, Católica Porto Business School, Universidade Católica Portuguesa.
    2. repec:eee:jouret:v:92:y:2016:i:1:p:96-108 is not listed on IDEAS
    3. Amar Cheema & Peter Leszczyc & Rajesh Bagchi & Richard Bagozzi & James Cox & Utpal Dholakia & Eric Greenleaf & Amit Pazgal & Michael Rothkopf & Michael Shen & Shyam Sunder & Robert Zeithammer, 2005. "Economics, Psychology, and Social Dynamics of Consumer Bidding in Auctions," Marketing Letters, Springer, vol. 16(3), pages 401-413, December.
    4. Wilfred Amaldoss & Sanjay Jain, 2008. "Joint Bidding in the Name-Your-Own-Price Channel: A Strategic Analysis," Management Science, INFORMS, vol. 54(10), pages 1685-1699, October.
    5. Ernan Haruvy & Peter Popkowski Leszczyc & Octavian Carare & James Cox & Eric Greenleaf & Wolfgang Jank & Sandy Jap & Young-Hoon Park & Michael Rothkopf, 2008. "Competition between auctions," Marketing Letters, Springer, vol. 19(3), pages 431-448, December.
    6. Kevin Hasker & Robin Sickles, 2010. "eBay in the Economic Literature: Analysis of an Auction Marketplace," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 37(1), pages 3-42, August.
    7. Amar Cheema & Dipankar Chakravarti & Atanu R. Sinha, 2012. "Bidding Behavior in Descending and Ascending Auctions," Marketing Science, INFORMS, vol. 31(5), pages 779-800, September.
    8. Gonçalves, Ricardo & Ray, Indrajit, 2017. "Partition Equilibria in a Japanese-English Auction with Discrete Bid Levels for the Wallet Game," CRETA Online Discussion Paper Series 34, Centre for Research in Economic Theory and its Applications CRETA.
    9. Peter T. L. Popkowski Leszczyc & Michael H. Rothkopf (deceased), 2010. "Charitable Motives and Bidding in Charity Auctions," Management Science, INFORMS, vol. 56(3), pages 399-413, March.
    10. Bruce L. Alford & Otis W. Gilley & Charles M. Wood & Obinna Obilo, 2017. "“No sale” items in auctions: do they really matter?," Marketing Letters, Springer, vol. 28(1), pages 155-168, March.
    11. repec:eee:jouret:v:90:y:2014:i:4:p:445-462 is not listed on IDEAS
    12. repec:eee:ecolet:v:159:y:2017:i:c:p:177-179 is not listed on IDEAS
    13. Reynolds, Kristy E. & Gilkeson, James H. & Niedrich, Ronald W., 2009. "The influence of seller strategy on the winning price in online auctions: A moderated mediation model," Journal of Business Research, Elsevier, vol. 62(1), pages 22-30, January.
    14. Wei Lim & Joo Lee-Partridge & Soo Tan, 2008. "Revenue implication of auction value in k-price sealed-bid auctions: An experimental study," Marketing Letters, Springer, vol. 19(1), pages 25-38, March.
    15. Richard Engelbrecht-Wiggans & Ernan Haruvy & Elena Katok, 2007. "A Comparison of Buyer-Determined and Price-Based Multiattribute Mechanisms," Marketing Science, INFORMS, vol. 26(5), pages 629-641, 09-10.
    16. Scott Fay & Juliano Laran, 2009. "Implications of Expected Changes in the Seller's Price in Name-Your-Own-Price Auctions," Management Science, INFORMS, vol. 55(11), pages 1783-1796, November.
    17. Gonçalves, Ricardo & Ray, Indrajit, 2016. "Equilibria in a Japanese-English Auction with Discrete Bid Levels for the Wallet Game," Cardiff Economics Working Papers E2016/13, Cardiff University, Cardiff Business School, Economics Section.


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