Song Zuo

Song Zuo

Authored Publications
Sort By
  • Title
  • Title, descending
  • Year
  • Year, descending
    Preview abstract 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. View details
    Mechanism Design for Large Language Models
    Paul Duetting
    Haifeng Xu
    Proceedings of the ACM on Web Conference 2024, Association for Computing Machinery, New York, NY, USA, 144–155
    Preview abstract We investigate auction mechanisms for AI-generated content, focusing on applications like ad creative generation. In our model, agents' preferences over stochastically generated content are encoded as large language models (LLMs). We propose an auction format that operates on a token-by-token basis, and allows LLM agents to influence content creation through single dimensional bids. We formulate two desirable incentive properties and prove their equivalence to a monotonicity condition on output aggregation. This equivalence enables a second-price rule design, even absent explicit agent valuation functions. Our design is supported by demonstrations on a publicly available LLM. View details
    Preview abstract 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. View details
    Preview abstract 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. View details
    Preview abstract In this survey, we summarize recent developments in research fueled by the growing adoption of automated bidding strategies in online advertising. We explore the challenges and opportunities that have arisen as markets embrace this autobidding and cover a range of topics in this area, including bidding algorithms, equilibrium analysis and efficiency of common auction formats, and optimal auction design. View details
    Complex Dynamics in Autobidding Systems
    Georgios Piliouras
    Kelly Spendlove
    Proceedings of the 25th ACM Conference on Economics and Computation (2024)
    Preview abstract It has become the default in markets such as ad auctions for participants to bid in an auction through automated bidding agents (autobidders) which adjust bids over time to satisfy return-over-spend constraints. Despite the prominence of such systems for the internet economy, their resulting dynamical behavior is still not well understood. Although one might hope that such relatively simple systems would typically converge to the equilibria of their underlying auctions, we provide a plethora of results that show the emergence of complex behavior, such as bi-stability, periodic orbits and quasi periodicity. We empirically observe how the market structure (expressed as motifs) qualitatively affects the behavior of the dynamics. We complement it with theoretical results showing that autobidding systems can simulate both linear dynamical systems as well logical boolean gates. View details
    Preview abstract 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. View details
    Preview abstract 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. View details
    Calibrated Click-Through Auctions
    Dirk Bergemann
    Paul Duetting
    Proceedings of the ACM Web Conference 2022, pp. 47-57
    Preview abstract We analyze the optimal information design in a click-through auction with stochastic click-through rates and known valuations per click. The auctioneer takes as given the auction rule of the click-through auction, namely the generalized second-price auction. Yet, the auctioneer can design the information flow regarding the click-through rates among the bidders. We require that the information structure to be calibrated in the learning sense. With this constraint, the auction needs to rank the ads by a product of the value and a calibrated prediction of the click-through rates. The task of designing an optimal information structure is thus reduced to the task of designing an optimal calibrated prediction. We show that in a symmetric setting with uncertainty about the click-through rates, the optimal information structure attains both social efficiency and surplus extraction. The optimal information structure requires private (rather than public) signals to the bidders. It also requires correlated (rather than independent) signals, even when the underlying uncertainty regarding the click-through rates is independent. Beyond symmetric settings, we show that the optimal information structure requires partial information disclosure, and achieves only partial surplus extraction. View details
    Preview abstract Online advertisements are primarily sold via repeated auctions with reserve prices. In this paper, we study how to set reserves to boost revenue based on the historical bids of strategic buyers, while controlling the impact of such a policy on the incentive compatibility of the repeated auctions. Adopting an incentive compatibility metric which quantifies the incentives to shade bids, we propose a novel class of reserve pricing policies and provide analytical tradeoffs between their revenue performance and bid-shading incentives. The policies are inspired by the exponential mechanism from the literature on differential privacy, but our study uncovers mechanisms with significantly better revenue-incentive tradeoffs than the exponential mechanism in practice. We further empirically evaluate the tradeoffs on synthetic data as well as ad auction data from a major ad exchange to verify and support our theoretical findings. View details