Modeling Price Dynamics in eBay Auctions Using Principal Differential Analysis

Abstract

Empirical research of online auctions has dramatically grown in recent years. Studies using publicly available bid data from websites such as eBay.com have found many divergences of bidding behavior and auction outcomes compared to ordinary offline auctions and auction theory. Among the main differences between online and offline auctions is their longer duration (typically a few days). Along with the anonymity of bidders and sellers and the low barriers of entry, the longer online auctions tend to exhibit variable dynamics both in the bid arrivals and in the price process. In this paper we propose a family of differential equations models that captures the dynamics in online auctions. We show that a second-order differential equation well-approximates the three-phase dynamics that take place during an eBay auction. We then propose a novel multiple-comparisons test to compare dynamic models of auction sub-populations, where the population grouping is based on characteristics of the auction, the item, the seller, and the bidders. We accomplish the modeling task within the framework of principal differential analysis and functional data models.

Keywords: Auction dynamics, functional data analysis, differential equation, price curve, multiple comparisons