Setting Reserve Prices in Second-Price Auctions with Unobserved Bids

Abstract

In this work we consider a seller who sells an item via second-price auctions with a reserve price. By controlling the reserve price, the seller can influence the revenue from the auction, and in this paper, we propose a method for learning optimal reserve prices. We study a limited information setting where the probability distribution of the bids from bidders is unknown and the values of the bids are not revealed to the seller. Furthermore, we do not assume that the seller has access to a historical data set with bids. Our main contribution is a method that incorporates knowledge about the rules of second-price auctions into a multiarmed bandit framework for optimizing reserve prices in our limited information setting. The proposed method can be applied in both stationary and nonstationary environments. Experiments show that the proposed method outperforms state-of-the-art bandit algorithms. In stationary environments, our method outperforms these algorithms when the horizon is short and performs as good as they do for longer horizons. Our method is especially useful if there is a high number of potential reserve prices. In addition, our method adapts quickly to changing environments and outperforms state-of-the-art bandit algorithms designed for nonstationary environments. Summary of Contribution: A key challenge in online advertising is the pricing of advertisements in online auctions. The scope of our study is second-price auctions with a focus on the reserve price optimization problem from a seller’s point of view. This problem is motivated by the real-life practice of small and medium-sized web publishers. However, the proposed solution approach is applicable to any seller who sells an item via second-price auctions and wants to optimize its reserve price during these auctions. Our solution approach is based on techniques from machine learning and operations research, and it would be beneficial especially for sellers who start the selling process without any historical data and can collect the data on the outcomes of the auctions while making reserve price decisions over time. History: Accepted by RamRamesh, Area Editor for Data Science & Machine Learning. Supplemental Material: The supplementary material is available at https://doi.org/10.1287/ijoc.2022.1199 .