We study the problem of auction design for advertising platforms that face strategic advertisers who are bidding across platforms. Each advertiser's goal is to maximize their total value or conversions while satisfying some constraint(s) across all the platforms they participates in. In this paper, we focus on advertisers with return-over-investment (henceforth, ROI) constraints, i.e. each advertiser is trying to maximize value while making sure that their ROI across all platforms is no less than some target value. An advertiser interacts with the platforms through autobidders -- for each platform, the advertiser strategically chooses a target ROI to report to the platform's autobidder, which in turn uses a uniform bid multiplier to bid on the advertiser's behalf on the queries owned by the given platform.

Online advertising platforms must decide how to allocate multiple ads across limited screen real estate, where each ad's effectiveness depends not only on its own placement but also on nearby ads competing for user attention. Such spatial externalities — arising from proximity, clutter, or crowding — can significantly alter welfare and revenue outcomes, yet existing auction and allocation models typically treat ad slots as independent or ordered along a single dimension.

We study the problem of finding the optimal bidding strategy for an advertiser in a multi-platform auction setting. The competition on a platform is captured by a value and a cost function, mapping bidding strategies to value and cost respectively. We assume a diminishing returns property, whereby the marginal cost is increasing in value. The advertiser uses an autobidder that selects a bidding strategy for each platform, aiming to maximize total value subject to budget and return-on-spend constraint. The advertiser has no prior information and learns about the value and cost functions by querying a platform with a specific bidding strategy. Our goal is to design algorithms that find the optimal bidding strategy with a small number of queries.

Advertisers are increasingly using automated bidding to optimize their ad campaigns on online advertising platforms. Autobidding allows an advertiser to optimize her objective subject to various constraints. In this paper, we design online autobidding algorithms to optimize value subject to ROI and budget constraints.

We study the worst-case welfare of item pricing in the tollbooth problem. The problem was first introduced by Guruswami et al. [27], and is a special case of the combinatorial auction in which (i) each of the m items in the auction is an edge of some underlying graph; and (ii) each of the n buyers is single-minded and only interested in buying all edges of a single path. We consider the competitive ratio between the hindsight optimal welfare and the optimal worst-case welfare among all item-pricing mechanisms, when the order of the arriving buyers is adversarial. We assume that buyers own the tie-breaking power, i.e. they can choose whether or not to buy the demand path at 0 utility. We prove a tight competitive ratio of 3/2 when the underlying graph is a single path (also known as the highway problem), whereas item-pricing can achieve the hindsight optimal if the seller is allowed to choose a proper tie-breaking rule to maximize the welfare [6, 11]. Moreover, we prove an O(1) upper bound of competitive ratio when the underlying graph is a tree.

In this paper, we address the important issue of uncertainty in the edge influence probability estimates for the well studied influence maximization problem --- the task of finding k seed nodes in a social network to maximize the influence spread. We propose the problem of robust influence maximization, which maximizes the worst-case ratio between the influence spread of the chosen seed set and the optimal seed set, given the uncertainty of the parameter input. We design an algorithm that solves this problem with a solution-dependent bound. We further study uniform sampling and adaptive sampling methods to effectively reduce the uncertainty on parameters and improve the robustness of the influence maximization task. Our empirical results show that parameter uncertainty may greatly affect influence maximization performance and prior studies that learned influence probabilities could lead to poor performance in robust influence maximization due to relatively large uncertainty in parameter estimates, and information cascade based adaptive sampling method may be an effective way to improve the robustness of influence maximization.