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We study a seller who sells a single good to multiple bidders with uncertainty over the joint distribution of bidders' valuations, as well as bidders' higher-order beliefs about their opponents. The seller only knows the (possibly…

Theoretical Economics · Economics 2022-02-16 Ethan Che

Designing revenue optimal auctions for selling an item to $n$ symmetric bidders is a fundamental problem in mechanism design. Myerson (1981) shows that the second price auction with an appropriate reserve price is optimal when bidders'…

Computer Science and Game Theory · Computer Science 2015-07-30 Hu Fu , Nicole Immolica , Brendan Lucier , Philipp Strack

We study a contextual version of the repeated brokerage problem. In each interaction, two traders with private valuations for an item seek to buy or sell based on the learner's-a broker-proposed price, which is informed by some contextual…

Machine Learning · Statistics 2025-03-11 François Bachoc , Tommaso Cesari , Roberto Colomboni

We propose a new architecture to approximately learn incentive compatible, revenue-maximizing auctions from sampled valuations. Our architecture uses the Sinkhorn algorithm to perform a differentiable bipartite matching which allows the…

Computer Science and Game Theory · Computer Science 2021-06-16 Michael J. Curry , Uro Lyi , Tom Goldstein , John Dickerson

We study revenue optimization learning algorithms for repeated posted-price auctions where a seller interacts with a single strategic buyer that holds a fixed private valuation for a good and seeks to maximize his cumulative discounted…

Computer Science and Game Theory · Computer Science 2018-02-09 Alexey Drutsa

The growing demand for data and AI-generated digital goods, such as personalized written content and artwork, necessitates effective pricing and feedback mechanisms that account for uncertain utility and costly production. Motivated by…

Computer Science and Game Theory · Computer Science 2023-06-06 Zachary Robertson , Oluwasanmi Koyejo

In this paper, we study the problem of learning to bid in repeated first-price auctions with budget constraints. In each period, the decision maker needs to submit a bid to win the auction and maximize the total collected reward, subject to…

Optimization and Control · Mathematics 2026-03-10 Zeng Fu , Jiashuo Jiang , Yuan Zhou

In markets such as digital advertising auctions, bidders want to maximize value rather than payoff. This is different to the utility functions typically assumed in auction theory and leads to different strategies and outcomes. We refer to…

Computer Science and Game Theory · Computer Science 2016-07-14 Salman Fadaei , Martin Bichler

Existing auto-bidding algorithms in digital advertising often treat the value of an ad opportunity as the revenue obtained when an ad is shown and/or clicked, and bid accordingly. This can lead to wasteful spending because the true value is…

Computer Science and Game Theory · Computer Science 2026-05-05 Yuxiao Wen , Zihao Hu , Yanjun Han , Yuan Yao , Zhengyuan Zhou

We study reserve price optimization in multi-phase second price auctions, where the seller's prior actions affect the bidders' later valuations through a Markov Decision Process (MDP). Compared to the bandit setting in existing works, the…

Machine Learning · Computer Science 2026-03-04 Rui Ai , Boxiang Lyu , Zhaoran Wang , Zhuoran Yang , Michael I. Jordan

The study of repeated interactions between a learner and a utility-maximizing optimizer has yielded deep insights into the manipulability of learning algorithms. However, existing literature primarily focuses on independent, unlinked…

Computer Science and Game Theory · Computer Science 2026-04-10 Giannis Fikioris , Balasubramanian Sivan , Éva Tardos

The transition of display ad exchanges from second-price auctions (SPA) to first-price auctions (FPA) has raised questions about its impact on revenue. Auction theory predicts the revenue equivalence between these two auction formats.…

Computer Science and Game Theory · Computer Science 2024-12-04 Martin Bichler , Alok Gupta , Matthias Oberlechner

Bilateral trade models the problem of intermediating between two rational agents -- a seller and a buyer -- both characterized by a private valuation for an item they want to trade. We study the online learning version of the problem, in…

Computer Science and Game Theory · Computer Science 2024-09-04 Martino Bernasconi , Matteo Castiglioni , Andrea Celli , Federico Fusco

We present an extensive analysis of the key problem of learning optimal reserve prices for generalized second price auctions. We describe two algorithms for this task: one based on density estimation, and a novel algorithm benefiting from…

Machine Learning · Computer Science 2015-06-10 Mehryar Mohri , Andres Munoz Medina

First-price auctions have very recently swept the online advertising industry, replacing second-price auctions as the predominant auction mechanism on many platforms. This shift has brought forth important challenges for a bidder: how…

Machine Learning · Computer Science 2025-09-26 Yanjun Han , Zhengyuan Zhou , Aaron Flores , Erik Ordentlich , Tsachy Weissman

Bilateral trade models the task of intermediating between two strategic agents, a seller and a buyer, willing to trade a good for which they hold private valuations. We study this problem from the perspective of a broker, in a regret…

Computer Science and Game Theory · Computer Science 2025-09-29 Simone Di Gregorio , Paul Dütting , Federico Fusco , Chris Schwiegelshohn

Most of the work in the auction design literature assumes that bidders behave rationally based on the information available for every individual auction, and the revelation principle enables designers to restrict their efforts to incentive…

Computer Science and Game Theory · Computer Science 2024-05-14 Juncheng Li , Pingzhong Tang

We study repeated first-price auctions and general repeated Bayesian games between two players, where one player, the learner, employs a no-regret learning algorithm, and the other player, the optimizer, knowing the learner's algorithm,…

Computer Science and Game Theory · Computer Science 2024-02-14 Aviad Rubinstein , Junyao Zhao

We consider a multi-round auction setting motivated by pay-per-click auctions for Internet advertising. In each round the auctioneer selects an advertiser and shows her ad, which is then either clicked or not. An advertiser derives value…

Data Structures and Algorithms · Computer Science 2013-06-05 Moshe Babaioff , Yogeshwer Sharma , Aleksandrs Slivkins

We study repeated bilateral trade where an adaptive $\sigma$-smooth adversary generates the valuations of sellers and buyers. We provide a complete characterization of the regret regimes for fixed-price mechanisms under different feedback…

Machine Learning · Computer Science 2024-02-20 Nicolò Cesa-Bianchi , Tommaso Cesari , Roberto Colomboni , Federico Fusco , Stefano Leonardi