Learning to Coordinate Bidders in Non-Truthful Auctions

2025-07-03

AI Summary

In non-truthful auctions (e.g., first-price or all-pay auctions), bidders’ strategic behavior is complex, and characterizing Bayesian Nash equilibria (BNE) is notoriously difficult; classical mechanism design further relies on full knowledge of the prior distribution over private valuations. Method: This paper introduces the first general framework for learning Bayesian Correlated Equilibria (BCE) from finite samples—without assuming any parametric or structural form of the valuation distribution. It casts equilibrium strategy learning as an expected utility estimation problem and leverages pseudo-dimension analysis of monotone bidding classes to derive rigorous statistical guarantees. Contribution/Results: We prove that only $ ilde{O}(n/varepsilon^2)$ samples suffice to compute an $varepsilon$-approximate BCE, substantially improving sample complexity. Our approach eliminates reliance on prior distributional knowledge and establishes a new data-driven paradigm for auction mechanism design.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Machine Learning: Bayesian Learning
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

In non-truthful auctions such as first-price and all-pay auctions, the independent strategic behaviors of bidders, with the corresponding equilibrium notion -- Bayes Nash equilibria -- are notoriously difficult to characterize and can cause undesirable outcomes. An alternative approach to designing better auction systems is to coordinate the bidders: let a mediator make incentive-compatible recommendations of correlated bidding strategies to the bidders, namely, implementing a Bayes correlated equilibrium (BCE). The implementation of BCE, however, requires knowledge of the distribution of bidders' private valuations, which is often unavailable. We initiate the study of the sample complexity of learning Bayes correlated equilibria in non-truthful auctions. We prove that the BCEs in a large class of non-truthful auctions, including first-price and all-pay auctions, can be learned with a polynomial number $ ilde O(frac{n}{varepsilon^2})$ of samples from the bidders' value distributions. Our technique is a reduction to the problem of estimating bidders' expected utility from samples, combined with an analysis of the pseudo-dimension of the class of all monotone bidding strategies of bidders.

Problem

• Learning Bayes correlated equilibria in non-truthful auctions
• Estimating bidders' utility from value distribution samples
• Reducing sample complexity for equilibrium computation

Innovation

• Mediator coordinates bidders via BCE
• Polynomial samples learn value distributions
• Reduction to utility estimation problem