Jieming Mao
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Non-uniform Bid-scaling and Equilibria for Different Auctions: An Empirical Study
Proceedings of the ACM on Web Conference 2024, 256–266
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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.
All these price of anarchy results have been focused on welfare approximation in the worst-case scenarios. To complement theoretical understandings, we empirically study how different auction formats (FPA, GSP, VCG) with different levels of non-uniform bid-scaling perform in an autobidding world with a synthetic dataset for auctions. Our empirical findings include: * For both uniform bid-scaling and non-uniform bid-scaling, FPA is better than GSP and GSP is better than VCG in terms of both welfare and profit; * A higher level of non-uniform bid-scaling leads to lower welfare performance in both FPA and GSP, while different levels of non-uniform bid-scaling have no effect in VCG. Our methodology of synthetic data generation may be of independent interest.
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Optimal Mechanisms for a Value Maximizer: The Futility of Screening Targets
Proceedings of the 25th ACM Conference on Economics and Computation (EC)(2024)
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Motivated by the increased adoption of autobidding algorithms in internet advertising markets, we study the design of optimal mechanisms for selling items to a value-maximizing buyer with a return-on-spend constraint. The buyer's values and target ratio in the return-on-spend constraint are private. We restrict attention to deterministic sequential screening mechanisms that can be implemented as a menu of prices paid for purchasing an item or not. The main result of this paper is to provide a characterization of an optimal mechanism. Surprisingly, we show that the optimal mechanism does not require target screening, i.e., offering a single pair of prices is optimal for the seller. The optimal mechanism is a subsidized posted price that provides a subsidy to the buyer to encourage participation and then charges a fixed unit price for each item sold. The seller's problem is a challenging non-linear mechanism design problem, and a key technical contribution of our work is to provide a novel approach to analyze non-linear pricing contracts.
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Efficiency of the Generalized Second-Price Auction for Value Maximizers
Hanrui Zhang
Proceedings of the ACM on Web Conference 2024, 46–56
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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.
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Autobidding Auctions in the Presence of User Costs
Hanrui Zhang
Proceedings of the ACM Web Conference 2023, pp. 3428-3435
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Although costs are prevalent in ad auctions, not many auction theory works study auction design in the presence of cost in the classic settings. One reason is that most auctions design in the setting without cost directly generalize to the setting with cost when the bidders maximizing quasi-linear utility.
However, as auto-bidding becomes a major choice of advertisers in online advertising, the distinction from the underlying behavior model often leads to different solutions of many well-studied auctions. In the context of ad auctions with cost, VCG achieves optimal welfare with quasi-linear utility maximizing bidders, while has 0 welfare approximation guarantee with value maximizing bidders who follow the optimization behind common auto-bidding algorithms.
In this paper, we prove that the approximation welfare guarantee of VCG auction can be significantly improved by a minimal change --- introducing cost multipliers. We note that one can use either one multiplier per auction or one multiplier per bidder, but one global multiplier across all auctions and bidders does not work. Finally, to echo with our theoretical results, we conduct empirical evaluations using semi-synthetic data derived from real auction data of a major advertising platform.
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Optimal Pricing Schemes for an Impatient Buyer
Kangning Wang
Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms(2023), pp. 382-398
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A patient seller aims to sell a good to an impatient buyer (i.e., one who discounts utility over time).The buyer will remain in the market for a period of time T , and her private value is drawn from a publicly known distribution. What is the revenue-optimal pricing-curve (sequence of (price, time) pairs) for the seller? Is randomization of help here? Is the revenue-optimal pricing-curve computable in polynomial time? We answer these questions in this paper. We give an efficient algorithm for computing the revenue-optimal pricing curve. We show that pricing curves, that post a price at each point of time and let the buyer pick her utility maximizing time to buy, are revenue-optimal among a much broader class of sequential lottery mechanisms: namely, mechanisms that allow the seller to post a menu of lotteries at each point of time cannot get any higher revenue than pricing curves. We also show that the even broader class of mechanisms that allow the menu of lotteries to be adaptively set, can earn strictly higher revenue than that of pricing curves, and the revenue gap can be as big as the support size of the buyer’s value distribution.
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The streaming model of computation is a popular approach for working with large-scale data. In this setting, there is a stream of items and the goal is to compute the desired quantities (usually data statistics) while making a single pass through the stream and using as little space as possible.
Motivated by the importance of data privacy, we develop differentially private streaming algorithms under the continual release setting, where the union of outputs of the algorithm at every timestamp must be differentially private. Specifically, we study the fundamental $\ell_p$ $(p\in [0,+\infty))$ frequency moment estimation problem under this setting, and give an $\varepsilon$-DP algorithm that achieves $(1+\eta)$-relative approximation $(\forall \eta\in(0,1))$ with $\mathrm{poly}\log(Tn)$ additive error and uses $\mathrm{poly}\log(Tn)\cdot \max(1, n^{1-2/p})$ space, where $T$ is the length of the stream and $n$ is the size of the universe of elements.
Our space is near optimal up to poly-logarithmic factors even in the non-private setting.
To obtain our results, we first reduce several primitives under the differentially private continual release model, such as counting distinct elements, heavy hitters and counting low frequency elements, to the simpler, counting/summing problems in the same setting.
Based on these primitives, we develop a differentially private continual release level set estimation approach to address the $\ell_p$ frequency moment estimation problem.
We also provide a simple extension of our results to the harder sliding window model, where the statistics must be maintained over the past $W$ data items.
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Approximately Efficient Bilateral Trade
Kangning Wang
Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing(2022), 718–721
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We study bilateral trade between two strategic agents. The celebrated result of Myerson and Satterthwaite states that in general, no incentive-compatible, individually rational and weakly budget balanced mechanism can be efficient. I.e., no mechanism with these properties can guarantee a trade whenever buyer value exceeds seller cost. Given this, a natural question is whether there exists a mechanism with these properties that guarantees a constant fraction of the first-best gains-from-trade, namely a constant fraction of the gains-from-trade attainable whenever buyer’s value weakly exceeds seller’s cost. In this work, we positively resolve this long-standing open question on constant-factor approximation, mentioned in several previous works, using a simple mechanism that obtains a 1/8.23 ≈ 0.121 fraction of the first-best.
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In shuffle privacy, each user sends a collection of randomized messages to a trusted shuffler, the shuffler randomly permutes these messages, and the resulting shuffled collection of messages must satisfy differential privacy. Prior work in this model has largely focused on protocols that use a single round of communication to compute algorithmic primitives like means, histograms, and counts. In this work, we present interactive shuffle protocols for stochastic convex optimization. Our optimization protocols rely on a new noninteractive protocol for summing vectors of bounded $\ell_2$ norm. By combining this sum subroutine with accelerated gradient descent, Nesterov's smoothing method, and a careful alignment of noise level and mini-batch size, we obtain loss guarantees that significantly improve on those of the local model and sometimes match those of the central model.
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Optimal Mechanisms for Value Maximizers with Budget Constraints via Target Clipping
Proceedings of the 23rd ACM Conference on Economics and Computation(2022), pp. 475
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We study the design of revenue-maximizing mechanisms for value-maximizing agents with budget constraints. Agents have return-on-spend constraints requiring a minimum amount of value per unit of payment made and budget constraints limiting their total payments. The agents' only private information are the minimum admissible ratios on the return-on-spend constraint, referred to as the target ratios.
Our work is motivated by internet advertising platforms, where automated bidders are increasingly being adopted by advertisers to purchase advertising opportunities on their behalf. Instead of specifying bids for each keyword, advertiser set high-level goals, such as maximizing clicks, and targets on cost-per-clicks or return-on-spend, and the platform automatically purchases opportunities by bidding in different auctions. We present a model that abstracts away the complexities of the auto-bidding procurement process that is general enough to accommodate many allocation mechanisms such as auctions, matchings, etc.
We reduce the mechanism design problem when agents have private target ratios to a challenging non-linear optimization problem with monotonicity constraints. We provide a novel decomposition approach to tackle this problem that yields insights into the structure of optimal mechanisms and show that surprising features stem from the interaction on budget and return-on-spend constraints. Our optimal mechanism, which we dub the target-clipping mechanism, has an appealing structure: it sets a threshold on the target ratio of each agent, targets above the threshold are allocated efficiently, and targets below are clipped to the threshold.
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In the shuffle model of differential privacy, data-holding users send randomized messages to a secure shuffler, the shuffler permutes the messages, and the resulting collection of messages must be differentially private with regard to user data. In the pan-private model, an algorithm processes a stream of data while maintaining an internal state that is differentially private with regard to the stream data. We give evidence connecting these two apparently different models.
Our results focus on robustly shuffle private protocols, whose privacy guarantees are not greatly affected by malicious users. First, we give robustly shuffle private protocols and upper bounds for counting distinct elements and uniformity testing. Second, we use pan-private lower bounds to prove robustly shuffle private lower bounds for both problems. Focusing on the dependence on the domain size k, we find that robust approximate shuffle privacy and approximate pan-privacy have additive error Θ(k^1/2) for counting distinct elements. For uniformity testing, we give a robust approximate shuffle private protocol with sample complexity O(k^2/3) and show that an Ω(k^2/3) dependence is necessary for any robust pure shuffle private tester. Finally, we show that this connection is useful in both directions: we give a pan-private adaptation of recent work on shuffle private histograms and use it to recover further separations between pan-privacy and interactive local privacy.
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