The BARISTA: A model for bid arrivals in online auctions

The arrival process of bidders and bids in online auctions is important for studying and modeling supply and demand in the online marketplace. A popular assumption in the online auction literature is that a Poisson bidder arrival process is a reasonable approximation. This approximation underlies theoretical derivations, statistical models and simulations used in field studies. However, when it comes to the bid arrivals, empirical research has shown that the process is far from Poisson, with early bidding and last-moment bids taking place. An additional feature that has been reported by various authors is an apparent self-similarity in the bid arrival process. Despite the wide evidence for the changing bidding intensities and the self-similarity, there has been no rigorous attempt at developing a model that adequately approximates bid arrivals and accounts for these features. The goal of this paper is to introduce a family of distributions that well-approximate the bid time distribution in hard-close auctions. We call this the BARISTA process (Bid ARrivals In STAges) because of its ability to generate different intensities at different stages. We describe the properties of this model, show how to simulate bid arrivals from it, and how to use it for estimation and inference. We illustrate its power and usefulness by fitting simulated and real data from eBay.com. Finally, we show how a Poisson bidder arrival process relates to a BARISTA bid arrival process.

💡 Research Summary

The paper addresses a long‑standing gap in the modeling of online auction dynamics: while the arrival of bidders is often assumed to follow a homogeneous Poisson process, empirical evidence shows that the timing of bids themselves is far from Poisson. Bids tend to cluster at the beginning of an auction, remain relatively sparse during the middle, and surge again just before the hard close. Moreover, several studies have reported a self‑similar (scale‑free) structure in the inter‑bid intervals, a feature that existing models do not capture. To fill this void, the authors introduce the BARISTA process—Bid ARrivals In STAges—a flexible family of non‑homogeneous Poisson processes specifically designed for hard‑close auctions.

Model Construction
The auction horizon (