We study the price of anarchy of first-price auctions in the autobidding world, where bidders can be either utility maximizers (i.e., traditional bidders) or value maximizers (i.e., autobidders).

Unlike the classic utility maximizers who maximize their quasi-linear utility given by the difference between value and payment, value maximizers maximize the total value subject to a return-on-spend (RoS) constraint [Balseiro et al., 2021b].

We consider the problem of designing contextual bandit algorithms in the "cross-learning" setting of Balseiro et al., where the learner observes the loss for the action

We consider the problem of designing contextual bandit algorithms in the "cross-learning" setting of Balseiro et al., where the learner observes the loss for the action

In the classical contextual bandits problem, in each roundt, a learner observes some contextc, chooses some actiona to perform, and receives some reward ra,t(c).

Wealso provide improvedregret bounds when theothers' maximum bid exhibits the further structure of sparsity.

We study the price of anarchy of first-price auctions in the autobidding world, where bidders can be either utility maximizers (i.e., traditional bidders) or value maximizers (i.e., autobidders). We show that with autobidders only, the price of anarchy of first-price auctions is $1/2$, and with both kinds of bidders, the price of anarchy degrades to about $0.457$ (the precise number is given by an optimization). These results complement the recent result by [Jin and Lu, 2022] showing that the price of anarchy of first-price auctions with traditional bidders is $1 - 1/e^2$. We further investigate a setting where the seller can utilize machine-learned advice to improve the efficiency of the auctions. There, we show that as the accuracy of the advice increases, the price of anarchy improves smoothly from about $0.457$ to $1$.

In non-truthful auctions such as first-price and all-pay auctions, the independent strategic behaviors of bidders, with the corresponding Bayes-Nash equilibrium notion, are notoriously difficult to characterize and can cause undesirable outcomes. An alternative approach to achieve better outcomes in non-truthful auctions is to coordinate the bidders: let a mediator make incentive-compatible recommendations of correlated bidding strategies to the bidders, namely, implementing a Bayes correlated equilibrium (BCE). The implementation of BCE, however, requires knowledge of the distributions of bidders' private valuations, which is often unavailable. We initiate the study of the sample complexity of learning Bayes correlated equilibria in non-truthful auctions. We prove that the set of strategic-form BCEs in a large class of non-truthful auctions, including first-price and all-pay auctions, can be learned with a polynomial number $\tilde O(\frac{n}{\varepsilon^2})$ of samples of bidders' values. This moderate number of samples demonstrates the statistical feasibility of learning to coordinate bidders. Our technique is a reduction to the problem of estimating bidders' expected utility from samples, combined with an analysis of the pseudo-dimension of the class of all monotone bidding strategies.

The E-commerce advertising platforms typically sell commercial traffic through either second-price auction (SPA) or first-price auction (FPA). SPA was historically prevalent due to its dominant strategy incentive-compatible (DSIC) for bidders with quasi-linear utilities, especially when budgets are not a binding constraint, while FPA has gained more prominence for offering higher revenue potential to publishers and avoiding the possibility for discriminatory treatment in personalized reserve prices. Meanwhile, on the demand side, advertisers are increasingly adopting platform-wide marketing solutions akin to QuanZhanTui, shifting from spending budgets solely on commercial traffic to bidding on the entire traffic for the purpose of maximizing overall sales. For automated bidding systems, such a trend poses a critical challenge: determining optimal strategies across heterogeneous auction channels to fulfill diverse advertiser objectives, such as maximizing return (MaxReturn) or meeting target return on ad spend (TargetROAS). To overcome this challenge, this work makes two key contributions. First, we derive an efficient solution for optimal bidding under FPA channels, which takes into account the presence of organic traffic - traffic can be won for free. Second, we introduce a marginal cost alignment (MCA) strategy that provably secures bidding efficiency across heterogeneous auction mechanisms. To validate performance of our developed framework, we conduct comprehensive offline experiments on public datasets and large-scale online A/B testing, which demonstrate consistent improvements over existing methods.

We study the price of anarchy of first-price auctions in the autobidding world, where bidders can be either utility maximizers (i.e., traditional bidders) or value maximizers (i.e., autobidders).