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We initiate the study of statistical inference and A/B testing for two market equilibrium models: linear Fisher market (LFM) equilibrium and first-price pacing equilibrium (FPPE). LFM arises from fair resource allocation systems such as…

Computer Science and Game Theory · Computer Science 2025-03-10 Luofeng Liao , Christian Kroer

Online A/B testing is widely used in the internet industry to inform decisions on new feature roll-outs. For online marketplaces (such as advertising markets), standard approaches to A/B testing may lead to biased results when buyers…

Motivated by autobidding systems in online advertising, we study revenue maximization in markets with divisible goods and budget-constrained buyers with linear valuations. Our aim is to compute a single price for each good and an allocation…

Computer Science and Game Theory · Computer Science 2026-02-17 Ioannis Caragiannis , Anders Bo Ipsen , Stratis Skoulakis

The linear Fisher market (LFM) is a basic equilibrium model from economics, which also has applications in fair and efficient resource allocation. First-price pacing equilibrium (FPPE) is a model capturing budget-management mechanisms in…

Statistics Theory · Mathematics 2025-03-11 Luofeng Liao , Christian Kroer

In this paper, we investigate the computation of second-price pacing equilibria (SPPEs), a foundational model in online advertising auctions. We present a polynomial-time algorithm for computing exact SPPEs in instances with a constant…

Computer Science and Game Theory · Computer Science 2026-05-12 Yiyang Huang , Yonglei Yan , Zihe Wang , Zhengyang Liu

The internet advertising market is a multi-billion dollar industry, in which advertisers buy thousands of ad placements every day by repeatedly participating in auctions. An important and ubiquitous feature of these auctions is the presence…

Computer Science and Game Theory · Computer Science 2022-10-11 Santiago Balseiro , Christian Kroer , Rachitesh Kumar

Mature internet advertising platforms offer high-level campaign management tools to help advertisers run their campaigns, often abstracting away the intricacies of how each ad is placed and focusing on aggregate metrics of interest to…

Computer Science and Game Theory · Computer Science 2021-09-07 Vincent Conitzer , Christian Kroer , Debmalya Panigrahi , Okke Schrijvers , Eric Sodomka , Nicolas E. Stier-Moses , Chris Wilkens

First price auctions are widely used in government contracts and industrial auctions. In this paper, we consider the Bayesian Nash Equilibrium (BNE) in first price auctions with discrete value distributions. We study the characterization of…

Computer Science and Game Theory · Computer Science 2019-07-10 Weiran Shen , Zihe Wang , Song Zuo

We provide efficient estimation methods for first- and second-price auctions under independent (asymmetric) private values and partial observability. Given a finite set of observations, each comprising the identity of the winner and the…

Computer Science and Game Theory · Computer Science 2022-05-05 Yeshwanth Cherapanamjeri , Constantinos Daskalakis , Andrew Ilyas , Manolis Zampetakis

In many first-price auctions, bidders face considerable strategic uncertainty: They cannot perfectly anticipate the other bidders' bidding behavior. We propose a model in which bidders do not know the entire distribution of opponent bids…

Theoretical Economics · Economics 2022-03-30 Bernhard Kasberger

Throttling is a popular method of budget management for online ad auctions in which the platform modulates the participation probability of an advertiser in order to smoothly spend her budget across many auctions. In this work, we…

Computer Science and Game Theory · Computer Science 2023-02-07 Xi Chen , Christian Kroer , Rachitesh Kumar

We study the computational complexity of computing Bayes-Nash equilibria in first-price auctions with discrete value distributions and discrete bidding space, under general subjective beliefs. It is known that such auctions do not always…

Computer Science and Game Theory · Computer Science 2024-11-06 Aris Filos-Ratsikas , Yiannis Giannakopoulos , Alexandros Hollender , Charalampos Kokkalis

We consider the problem of computing a (pure) Bayes-Nash equilibrium in the first-price auction with continuous value distributions and discrete bidding space. We prove that when bidders have independent subjective prior beliefs about the…

Computer Science and Game Theory · Computer Science 2023-03-06 Aris Filos-Ratsikas , Yiannis Giannakopoulos , Alexandros Hollender , Philip Lazos , Diogo Poças

Our paper concerns the computation of Nash equilibria of first-price auctions with correlated values. While there exist several equilibrium computation methods for auctions with independent values, the correlation of the bidders' values…

Computer Science and Game Theory · Computer Science 2021-08-11 Benjamin Heymann , Panayotis Mertikopoulos

Statistical inference under market equilibrium effects has attracted increasing attention recently. In this paper we focus on the specific case of linear Fisher markets. They have been widely use in fair resource allocation of food/blood…

Econometrics · Economics 2025-02-19 Luofeng Liao , Yuan Gao , Christian Kroer

Online A/B testing, the gold standard for evaluating new advertising policies, consumes substantial engineering resources and risks significant revenue loss from deploying underperforming variations. This motivates the use of Off-Policy…

Machine Learning · Computer Science 2025-12-04 Hongseon Yeom , Jaeyoul Shin , Soojin Min , Jeongmin Yoon , Seunghak Yu , Dongyeop Kang

Computing market equilibria is a problem of both theoretical and applied interest. Much research to date focuses on the case of static Fisher markets with full information on buyers' utility functions and item supplies. Motivated by…

Computer Science and Game Theory · Computer Science 2021-10-05 Yuan Gao , Christian Kroer , Alex Peysakhovich

This paper tackles challenges in pricing and revenue projections due to consumer uncertainty. We propose a novel data-based approach for firms facing unknown consumer type distributions. Unlike existing methods, we assume firms only observe…

Theoretical Economics · Economics 2024-05-28 Duarte Gonçalves , Bruno A. Furtado

In non-truthful auctions, agents' utility for a strategy depends on the strategies of the opponents and also the prior distribution over their private types; the set of Bayes Nash equilibria generally has an intricate dependence on the…

Computer Science and Game Theory · Computer Science 2022-11-02 Hu Fu , Tao Lin

The first-price auction is popular in practice for its simplicity and transparency. Moreover, its potential virtues grow in complex settings where incentive compatible auctions may generate little or no revenue. Unfortunately, the…

Computer Science and Game Theory · Computer Science 2013-04-30 Darrell Hoy , Kamal Jain , Christopher A. Wilkens
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