Private Private Information in Second-Price Auction

2026-04-27

AI Summary

This study investigates how a seller in a second-price auction can achieve efficient allocation and near-optimal revenue by designing a private information structure, under the assumptions that bidders’ signals are ex ante independent and their valuations are symmetric and affiliated. Addressing the fragility of classical mechanisms to informational interdependence, the authors construct—for the first time—a private information structure that yields allocations arbitrarily close to the maximum social welfare and admits a strict Bayesian Nash equilibrium. They fully characterize the feasible frontier of (bidder surplus, seller revenue) pairs and establish necessary and sufficient conditions for bidder surplus to approach maximal welfare. The work further demonstrates that while full surplus extraction is theoretically possible, it leads to equilibrium instability, and proves the impossibility of exactly achieving maximum welfare under private information, delineating the precise boundary of this impossibility.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Privacy-enhancing technologies
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Classic results show that even an arbitrarily small correlation across bidders' information can enable full surplus extraction in auctions and related mechanism design settings. Motivated by this fragility, we study the information independence in a second-price auction when the seller commits to a private private information structure, meaning bidders' signals are independent ex ante, while bidders share a symmetric and arbitrarily correlated prior distribution over their valuations. We first show that the seller optimal efficient outcome with full surplus extraction can always be implemented by a private private information structure that admits a Bayes Nash equilibrium. However, this equilibrium may not be stable. We then further construct a private private information structure that achieves revenue arbitrarily close to maximum welfare while admitting a strict equilibrium. At the same time, we establish an impossibility result: under private private information, in general, bidder surplus cannot achieve maximal welfare exactly, and we characterize necessary and sufficient conditions on the prior distribution under which bidder surplus can be made arbitrarily close to maximal welfare. We then explore which other efficient outcomes are achievable under private private information. Finally, moving beyond private private information, we provide a complete characterization of the achievable pairs (bidder surplus, seller revenue) under general information structures.

Problem

• private private information
• second-price auction
• surplus extraction
• information structure
• Bayes Nash equilibrium

Innovation

• private private information
• second-price auction
• full surplus extraction
• strict equilibrium
• information structure