Empirical research of online auctions has grown dramatically in recent
years. Studies using publicly available bid data from such websites as
eBay.com have found many divergences of bidding behavior and auction
outcomes compared with ordinary offline auctions and auction theory.
Among the main differences between online and offline auctions are the
former’s longer duration, anonymity of bidders and sellers,
and low barriers of entry. All of these factors lead to dynamics in the
bid arrival and price process that change throughout the auction. In
this work we examine the price process in a large and diverse set of
eBay auctions, for both low- and high-valued items, in terms of item,
auction, bidder, and seller characteristics. We propose a family of
differential equation models that captures online auction dynamics. In particular, we show that a second-order linear differential equation
well approximates the dynamics that occur in our diverse set of
auctions. We also introduce a multiple-comparisons test for comparing dynamic models of
auction subpopulations, which we use to compare subpopulations of
auctions grouped by characteristics of the auction, item, seller, and
bidders. We find that price dynamics change throughout the auction and
are influenced mostly by factors that affect the level of uncertainty
about the outcome (e.g., seller rating, item condition) and the level
of competitiveness (e.g., early bidding, number of bids). We accomplish
the modeling tasks within the framework of principal differential
analysis and functional data models.