Estimating Functional Agent-Based Models: An Application to Bid Shading in Online Markets Format

Bid shading is a common strategy in online auctions to avoid the "winner’s curse". While almost all bidders shade their bids, at least to some degree, it is impossible to infer the degree and volume of shaded bids directly from observed bidding data. In fact, most bidding data only allows us to observe the resulting price process, i.e. whether prices increase fast (due to little shading) or whether they slow down (when all bidders shade their bids). In this work, we propose an agent-based model that simulates bidders with different bidding strategies and their interaction with one another. We calibrate that model (and hence estimate properties about the propensity and degree of shaded bids) by matching the emerging simulated price process with that of the observed auction data using genetic algorithms. From a statistical point of view, this is challenging because we match functional draws from simulated and real price processes. We propose several competing fitness functions and explore how the choice alters the resulting ABM calibration. We apply our model to the context of eBay auctions for digital cameras and show that a balanced fitness function yields the best results.