Modeling Price Dynamics in eBay Auctions Using Differential Equations
Bibliographic record
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.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".