First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper introduces the problem of repeated auctions with contextual information. Specifically, the auctioneer interacts with a single agent (at least in their initial model) who has a context vector x, corresponding to observable attributes, and a privately held weight vector w, such that the agent's value for the good is x*w. The goal of the auctioneer is to maximize the revenue from the posted price auction by learning w over time. However, the agent understand that the auctioneer may be adjusting prices based off of the his purchasing behavior, so he may lie (that is, not purchase the product even though it would give him positive surplus) in order to lower the price in future rounds.

Motivated by real-time advertising exchanges, we analyze the problem of pricing inventory in a repeated posted-price auction. We consider both the cases of a truthful and surplus-maximizing buyer, where the former makes decisions myopically on every round, and the latter may strategically react to our algorithm, forgoing short-term surplus in order to trick the algorithm into setting better prices in the future. We further assume a buyer's valuation of a good is a function of a context vector that describes the good being sold.

Motivated by real-time advertising exchanges, we analyze the problem of pricing inventory in a repeated posted-price auction. We consider both the cases of a truthful and surplus-maximizing buyer, where the former makes decisions myopically on every round, and the latter may strategically react to our algorithm, forgoing short-term surplus in order to trick the algorithm into setting better prices in the future. We further assume a buyer's valuation of a good is a function of a context vector that describes the good being sold.

Motivated by real-time advertising exchanges, we analyze the problem of pricing inventory in a repeated posted-price auction. We consider both the cases of a truthful and surplus-maximizing buyer, where the former makes decisions myopically on every round, and the latter may strategically react to our algorithm, forgoing short-term surplus in order to trick the algorithm into setting better prices in the future. We further assume a buyer’s valuation of a good is a function of a context vector that describes the good being sold. We give the first algorithm attaining sublinear (O(T^{2/3})) regret in the contextual setting against a surplus-maximizing buyer. We also extend this result to repeated second-price auctions with multiple buyers.