Is it possible to estimate the time required to reach your target bid?

Did you know that the number of eBay sellers in 2005 that considered online selling as their primary source of income was around 724,000 Americans?  These sellers are often looking to sell their goods as soon as they reach some target price.  They are more interested in a rapid turnaround of their capital than holding out for an extended period of time in the hope of obtaining a higher gain from a bidder.

I found this to be a very interesting trend and as I looked into it I discovered an interesting article; Estimating Time Required to Reach Bid Levels in OnlineAuctions by Subhajyoti and Seema Bandyopadhyay.   This article attempts to mathematically estimate the time required to reach a certain bid level in ongoing auctions.   This research looks into helping this type of sellers into reaching a pre-specified price.     

Online bidding greatly differs from a closed room-bidding environment.  The ladder only lasts a few hours while the former can span for several days.  The method used to categorize the bidding is the following.  After a bidder enters a bidding process, a bidder might check back on the auction.  This type of bidding involves every time a bidder logs into eBay to observe an ongoing auction.  When this happens, he or she might decide to make a higher bid or not.  The authors categorize this as an “interested observation” (event of visiting eBay and observing the current bid).  This event is estimated as a Poisson arrival process.     

The bidding process was modeled as a quasi-birth death (QBD) process.  Here is an explanation of how the authors used the “interested observations” to model this behavior:

“…because an auction page on eBay does not refresh automatically, an ‘interested observation’ can take place only when a new page view is registered…If the data recorded only one incremental page view between our polling, it meant that there were no new interested observations within the interval (the one page view was a result of the software’s polling).  If the data recorded two (or rarely, more) incremental page views, it meant that there was an interested observation within the polling interval.  By recording the bid price at that point in time, we then get to know (1) if the interested observation resulted in an increase in the bid and (2) how much was the increment in the bid.  Since we maintain the history of all the interested observations, we were able to observe whether a bid price increase from one interested observation resulted in a bid price increase in the next interested observation…and in a similar vein, if an interested observation that did not result in an increased bid would result in the next interested observation also not making an increased bid...” (Bandyopadhyay, Bandyopadhyay, p. 285-6, 2009).  

To view their mathematical methods, I invite you to read their interesting article. 

Post by:

Paulina Enrriquez Dominguez

Sources:

• http://toptenpk.com/wp-content/uploads/2013/01/Online-auction.png
• http://www.bluejay4n6.org/online%20auction.png
• http://investor.ebay.com/releasedetail.cfm?ReleaseID=170073
• http://uncc.worldcat.org/title/estimating-time-required-to-reach-bid-levels-in-online-auctions/oclc/4795488214&referer=brief_results