Modeling Price Dynamics in eBay Auctions Using Differential Equations

Abstract

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.