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 $O(\sqrt{T})$ 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 $O(\log T)$ 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.