We consider an extension to classic position auctions in which sponsored creatives are embedded within AI-generated content rather than shown in predefined slots. Leveraging advanced LLM technologies, it becomes viable to seamlessly integrate sponsored creatives with AI content and accurately estimate the context-aware benefits of differing insertion positions. However, this approach introduces novel challenges; substitution effects require rigorous treatment compared to standard position auction settings, where slots are independent of each other.

In the secretary problem, a set of secretary candidates arrive in a uniformly random order and reveal their values one by one. A company, who can only hire one candidate and hopes to maximize the expected value of its hire, needs to make irrevocable online decisions about whether to hire the current candidate. The classical framework of evaluating a policy is to compute its worst-case competitive ratio against the optimal solution in hindsight, and there the best policy -- the ''1/e law'' -- has a competitive ratio of 1/e. We propose an alternative evaluation framework through the lens of regret -- the worst-case additive difference between the optimal hindsight solution and the expected performance of the policy, assuming that each value is normalized between 0 and 1. The 1/e law for the classical framework has a regret of 1 - 1/e ≈ 0.632; by contrast, we show that the class of ''pricing curves'' algorithms can guarantee a regret of at most 1/4 = 0.25 (which is tight within the class), and the class of ''best-only pricing curves'' algorithms can guarantee a regret of at most 0.190 (with a lower bound of 0.171). In addition, we show that in general, no policy can give a regret guarantee better than 0.152. Finally, we discuss other objectives in our regret-minimization framework.

We study the price of anarchy of the generalized second-price auction where bidders are value maximizers (i.e., autobidders). We show that in general the price of anarchy can be as bad as 0. For comparison, the price of anarchy of running VCG is 1/2 in the autobidding world. We further show a fined-grained price of anarchy with respect to the discount factors (i.e., the ratios of click probabilities between lower slots and the highest slot in each auction) in the generalized second-price auction, which highlights the qualitative relation between the smoothness of the discount factors and the efficiency of the generalized second-price auction.

In recent years, the growing adoption of autobidding has motivated the study of auction design with value-maximizing auto-bidders. It is known that under mild assumptions, uniform bid-scaling is an optimal bidding strategy in truthful auctions, e.g., Vickrey-Clarke-Groves auction (VCG), and the price of anarchy for VCG is 2. However, for other auction formats like First-Price Auction (FPA) and Generalized Second-Price auction (GSP), uniform bid-scaling may not be an optimal bidding strategy, and bidders have incentives to deviate to adopt strategies with non-uniform bid-scaling. Moreover, FPA can achieve optimal welfare if restricted to uniform bid-scaling, while its price of anarchy becomes 2 when non-uniform bid-scaling strategies are allowed.

We study autobidding ad auctions with user costs, where each bidder is value-maximizing subject to a return-over-investment (ROI) constraint, and the seller aims to maximize the social welfare taking into consideration the user’s cost of viewing an ad. We show that in the worst case, the approximation ratio of social welfare by running the vanilla VCG auctions with user costs could as bad as 0. To improve the performance of VCG, We propose a new variant of VCG based on properly chosen cost multipliers, and prove that there exist auction-dependent and bidder-dependent cost multipliers that guarantee approximation ratios of 1/2 and 1/4 respectively in terms of the social welfare.

Auto-bidding has become one of the main options for bidding in online advertisements, in which advertisers only need to specify high-level objectives and leave the complex task of bidding to auto-bidders. In this paper, we propose a family of auctions with boosts to improve welfare in auto-bidding environments with both return on ad spend constraints and budget constraints. Our empirical results validate our theoretical findings and show that both the welfare and revenue can be improved by selecting the weight of the boosts properly.

It is common in recommendation systems that users both consume and produce information as they make strategic choices under uncertainty. While a social planner would balance “exploration” and “exploitation” using a multi-armed bandit algorithm, users' incentives may tilt this balance in favor of exploitation. We consider Bayesian Exploration: a simple model in which the recommendation system (the “principal”) controls the information flow to the users (the “agents”) and strives to incentivize exploration via information asymmetry. A single round of this model is a version of a well-known “Bayesian Persuasion game” from [24]. We allow heterogeneous users, relaxing a major assumption from prior work that users have the same preferences from one time step to another. The goal is now to learn the best personalized recommendations. One particular challenge is that it may be impossible to incentivize some of the user types to take some of the actions, no matter what the principal does or how much time she has. We consider several versions of the model, depending on whether and when the user types are reported to the principal, and design a near-optimal “recommendation policy” for each version. We also investigate how the model choice and the diversity of user types impact the set of actions that can possibly be “explored” by each type.

In consumer search, there is a set of items. An agent has a prior over her value for each item and can pay a cost to learn the instantiation of her value. After exploring a subset of items, the agent chooses one and obtains a payoff equal to its value minus the search cost. We consider a sequential model of consumer search in which agents' values are correlated and each agent updates her priors based on the exploration of past agents before performing her search. Specifically, we assume the value is the sum of a common-value component, called the quality, and a subjective score. Fixing the variance of the total value, we say a population is more diverse if the subjective score has a larger variance. We ask how diversity impacts average utility. We show that intermediate diversity levels yield significantly higher social utility than the extreme cases of no diversity (when agents under-explore) or full diversity (when agents are unable to learn from each other) and quantify how the impact of the diversity level changes depending on the time spent searching.