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 consider the problem of maximizing the gains from trade (GFT) in two-sided markets. The seminal impossibility result by Myerson and Satterthwaite (1983) shows that even for bilateral trade, there is no individually rational (IR), Bayesian incentive compatible (BIC) and budget balanced (BB) mechanism that can achieve the full GFT. Moreover, the optimal BIC, IR and BB mechanism that maximizes the GFT is known to be complex and heavily depends on the prior. In this paper, we pursue a Bulow-Klemperer-style question, i.e., does augmentation allow for prior-independent mechanisms to compete against the optimal mechanism? Our first main result shows that in the double auction setting with m i.i.d. buyers and n i.i.d. sellers, by augmenting O(1) buyers and sellers to the market, the GFT of a simple, dominant strategy incentive compatible (DSIC), and prior-independent mechanism in the augmented market is at least the optimal in the original market, when the buyers’ distribution first-order stochastically dominates the sellers’ distribution. The mechanism we consider is a slight variant of the standard Trade Reduction mechanism due to McAfee (1992). For comparison, Babaioff, Goldner, and Gonczarowski (2020) showed that if one is restricted to augmenting only one side of the market, then n(m + 4√m) additional agents are sufficient for their mechanism to beat the original optimal and ⌊ log2 m ⌋ additional agents are necessary for any prior-independent mechanism. Next, we go beyond the i.i.d. setting and study the power of two-sided recruitment in more general markets. Our second main result is that for any ε > 0 and any set of O(1/ε) buyers and sellers where the buyers’ value exceeds the sellers’ value with constant probability, if we add these additional agents into any market with arbitrary correlations, the Trade Reduction mechanism obtains a (1−ε)-approximation of the GFT of the augmented market. Importantly, the newly recruited agents are agnostic to the original market.

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.

We study the problem of selling information to a data-buyer who faces a decision problem under uncertainty. We consider the classic Bayesian decision-theoretic model pioneered by Blackwell. Initially, the data buyer has only partial information about the payoff-relevant state of the world. A data seller offers additional information about the state of the world. The information is revealed through signaling schemes, also referred to as experiments. In the single-agent setting, any mechanism can be represented as a menu of experiments. A recent paper by Bergemann et al.[8] present a complete characterization of the revenue-optimal mechanism in a binary state and binary action environment. By contrast, no characterization is known for the case with more actions. In this paper, we consider more general environments and study arguably the simplest mechanism, which only sells the fully informative experiment. In the environment with binary state and m≥3 actions, we provide an $O(m)$-approximation to the optimal revenue by selling only the fully informative experiment and show that the approximation ratio is tight up to an absolute constant factor. An important corollary of our lower bound is that the size of the optimal menu must grow at least linearly in the number of available actions, so no universal upper bound exists for the size of the optimal menu in the general single-dimensional setting. We also provide a sufficient condition under which selling only the fully informative experiment achieves the optimal revenue.

We study revenue maximization in multi-item multi-bidder auctions under the natural item-independence assumption – a classical problem in Multi-Dimensional Bayesian Mechanism Design. One of the biggest challenges in this area is developing algorithms to compute (approximately) optimal mechanisms that are not brute-force in the size of the bidder type space, which is usually exponential in the number of items in multi-item auctions. Unfortunately, such algorithms were only known for basic settings of our problem when bidders have unit-demand or additive valuations.

We study gains from trade in multi-dimensional two-sided markets. Specifically, we focus on a setting with n heterogeneous items, where each item is owned by a different seller i, and there is a constrained-additive buyer with feasibility constraint ℱ. Multi-dimensional settings in one-sided markets, e.g. where a seller owns multiple heterogeneous items but also is the mechanism designer, are well-understood. In addition, single-dimensional settings in two-sided markets, e.g. where a buyer and seller each seek or own a single item, are also well-understood. Multi-dimensional two-sided markets, however, encapsulate the major challenges of both lines of work: optimizing the sale of heterogeneous items, ensuring incentive-compatibility among both sides of the market, and enforcing budget balance. We present, to the best of our knowledge, the first worst-case approximation guarantee for gains from trade in a multi-dimensional two-sided market. Our first result provides an O(log(1/r))-approximation to the first-best gains from trade for a broad class of downward-closed feasibility constraints (such as matroid, matching, knapsack, or the intersection of these). Here r is the minimum probability over all items that a buyer's value for the item exceeds the seller's cost. Our second result removes the dependence on r and provides an unconditional O(log n)-approximation to the second-best gains from trade. We extend both results for a general constrained-additive buyer, losing another O(log n)-factor en-route. The first result is achieved using a fixed posted price mechanism, and the analysis involves a novel application of the prophet inequality or a new concentration inequality. Our second result follows from a stitching lemma that allows us to upper bound the second-best gains from trade by the first-best gains from trade from the “likely to trade” items (items with trade probability at least 1/n) and the optimal profit from selling the “unlikely to trade” items. We can obtain an O(log n)-approximation to the first term by invoking our O(log(1/r))-approximation on the “likely to trade” items. We introduce a generalization of the fixed posted price mechanism—seller adjusted posted price—to obtain an O(log n)-approximation to the optimal profit for the “unlikely to trade” items. Unlike fixed posted price mechanisms, not all seller adjusted posted price mechanisms are incentive compatible and budget balanced. We develop a new argument based on “allocation coupling” to show the seller adjusted posted price mechanism used in our approximation is indeed budget balanced and incentive-compatible.

We consider the black-box reduction from multidimensional revenue maximization to virtual welfare maximization. Cai et al. [12, 13, 14, 15] show a polynomial-time approximation-preserving reduction, however, the mechanism produced by their reduction is only approximately Bayesian incentive compatible (∊-BIC). We provide two new polynomial time transformations that convert any ∊-BIC mechanism to an exactly BIC mechanism with only a negligible revenue loss. Our first transformation applies to any mechanism design setting with downward-closed outcome space and only requires sample access to the agents' type distributions. Our second transformation applies to the fully general outcome space, removing the downward-closed assumption, but requires full access to the agents' type distributions. Both transformations only require query access to the original ∊-BIC mechanism. Other ∊-BIC to BIC transformations for revenue exist in the literature [23, 36, 18] but all require exponential time to run in both of the settings we consider. As an application of our transformations, we improve the reduction by Cai et al. [12, 13, 14, 15] to generate an exactly BIC mechanism.

The seminal impossibility result of Myerson and Satterthwaite [1983] states that for bilateral trade, there is no mechanism that is individually rational (IR), incentive compatible (IC), weakly budget balanced, and efficient. This has led follow-up work on two-sided trade settings to weaken the efficiency requirement and consider approximately efficient simple mechanisms, while still demanding the other properties. The current state-of-the-art of such mechanisms for two-sided markets can be categorized as giving one (but not both) of the following two types of approximation guarantees on the gains from trade : a constant ex-ante guarantee, measured with respect to the second-best efficiency benchmark, or an asymptotically optimal ex-post guarantee, measured with respect to the first-best efficiency benchmark. Here the second-best efficiency benchmark refers to the highest gains from trade attainable by any IR, IC and weakly budget balanced mechanism, while the first-best efficiency benchmark refers to the maximum gains from trade (attainable by the VCG mechanism, which is not weakly budget balanced).

We design simple mechanisms to approximate the Gains from Trade (GFT) in two-sided markets with multiple unit-supply sellers and multiple unit-demand buyers. A classical impossibility result by Myerson and Satterthwaite showed that even with only one seller and one buyer, no Bayesian Incentive Compatible (BIC), Individually Rational (IR), and Budget-Balanced (BB) mechanism can achieve full GFT (trade whenever buyer's value is higher than the seller's cost). The same paper also proposed the ``second-best'' mechanism that maximizes the GFT subject to BIC, IR, and BB constraints, which is unfortunately rather complex for even the single-seller single-buyer case. Our mechanism is simple, BIC, IR, and BB and achieves 1/2 of the optimal GFT among all BIC, IR, and BB mechanisms. The result holds for arbitrary distributions of the buyers' and sellers' values and can accommodate any downward-closed feasibility constraints over the allocations. The analysis of our mechanism is facilitated by extending the Cai-Weinberg-Devanur duality framework to two-sided markets.

We provide simple and approximately revenue-optimal mechanisms in the multi-item multi-bidder settings. We unify and improve all previous results, as well as generalize the results to broader cases. In particular, we prove that the better of the following two simple, deterministic and Dominant Strategy Incentive Compatible mechanisms, a sequential posted price mechanism or an anonymous sequential posted price mechanism with entry fee, achieves a constant fraction of the optimal revenue among all randomized, Bayesian Incentive Compatible mechanisms, when buyers' valuations are XOS over independent items. If the buyers' valuations are subadditive over independent items, the approximation factor degrades to O(logm), where m is the number of items. We obtain our results by first extending the Cai-Devanur-Weinberg duality framework to derive an effective benchmark of the optimal revenue for subadditive bidders, and then analyzing this upper bound with new techniques.

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.

Free will (or randomness) has been studied to achieve loophole-free Bell's inequality test and to provide device-independent quantum key distribution security proofs. The required randomness such that a local hidden variable model (LHVM) can violate the Clauser-Horne-Shimony-Holt (CHSH) inequality has been studied, but a tight bound has not been proved for a practical case that: 1) the device settings of the two parties in the Bell test are independent and 2) the device settings of each party can be correlated or biased across different runs. Using some information theoretic techniques, we prove, in this paper, a tight bound on the required randomness for this case, such that the CHSH inequality can be violated by certain LHVM. Our proof has a clear achievability and converse style. The achievability part is proved using type counting. To prove the converse part, we introduce a concept called profile for a set of binary sequences and study the properties of profiles. Our profile-based converse technique is also of independent interest.