Linear Program-Based Approximation for Personalized Reserve Prices

We study the problem of computing data-driven personalized reserve prices in eager second price auctions without having any assumption on valuation distributions. Here, the input is a data set that contains the submitted bids of n buyers in a set of auctions, and the problem is to return personalized reserve prices r that maximize the revenue earned on these auctions by running eager second price auctions with reserve r. For this problem, which is known to be NP complete, we present a novel linear program (LP) formulation and a rounding procedure, which achieves a 0.684 approximation. This improves over the [Formula: see text]-approximation algorithm from Roughgarden and Wang. We show that our analysis is tight for this rounding procedure. We also bound the integrality gap of the LP, which shows that it is impossible to design an algorithm that yields an approximation factor larger than 0.828 with respect to this LP.

Scalable Optimal Online Auctions

This paper provides a set of tools to compute and implement optimal reserve prices for online auctions.

Incentive-Compatible Learning of Reserve Prices for Repeated Auctions

How can an auctioneer optimize revenue by learning the reserve prices from the bids in the previous auctions? How should the long-term incentives and strategic behavior of the bidders be taken into account? Motivated in part by applications in online advertising, in “Incentive-Compatible Learning of Reserve Prices for Repeated Auctions,” Kanoria and Nazerzadeh investigate these questions. They show that if a seller attempts to dynamically update a common reserve price using the bidding history, buyers will shade their bids, which can hurt the revenue. However, when there is more than one buyer, using personalized reserve prices, the auctioneer can achieve a near-optimal revenue. In their proposed mechanism, the personal reserve price for each buyer is determined using the historical bids of other buyers.

Dynamic Incentive-Aware Learning: Robust Pricing in Contextual Auctions

In many practical settings, the decision makers have to learn their best actions by experimenting with possible options and collecting feedback (data) over time. It is often assumed that the collected data can be trusted as they reflect the ground truth. But this assumption is violated when the data are generated by strategic players. Consider online advertising market in which the ad exchange (decision maker) aims at learning the best reserve prices in the repeated auctions. In this setting, the data are advertisers’ submitted bids. Such data can be strategically corrupted by advertisers to trick the learning algorithm of the ad exchange to offer them lower reserve prices in the future auctions. In “Dynamic Incentive-Aware Learning: Robust Pricing in Contextual Auctions,” N. Golrezaei, A. Javanmard, and V. Mirrokni design effective learning algorithms with sublinear regret in such environments that are robust to the strategic behavior of the players.