Strategically-Robust Learning Algorithms for Bidding in First-Price Auctions

Learning to bid in repeated first-price auctions is a fundamental problem at the interface of game theory and machine learning, which has seen a recent surge in interest due to the transition of display advertising to first-price auctions. In this work, we propose a novel concave formulation for pure-strategy bidding in first-price auctions, and use it to analyze natural Gradient-Ascent-based algorithms for this problem. Importantly, our analysis goes beyond regret, which was the typical focus of past work, and also accounts for the strategic backdrop of online-advertising markets where bidding algorithms are deployed -- we prove that our algorithms cannot be exploited by a strategic seller and that they incentivize truth-telling for the buyer. Concretely, we show that our algorithms achieve O (T) regret when the highest competing bids are generated adversarially, and show that no online algorithm can do better. We further prove that the regret improves to O (T) when the competition is stationary and stochastic. Moving beyond regret, we show that a strategic seller cannot exploit our algorithms to extract more revenue on average than is possible under the optimal mechanism, i. e. , the seller cannot do much better than posting the monopoly reserve price in each auction. Finally, we prove that our algorithm is also incentive compatible -- it is a (nearly) dominant strategy for the buyer to report her values truthfully to the algorithm as a whole.