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Private From Whom? Minimal Information Leakage in Auctions

Eric Gao, Eric Tang

TL;DR

This work provides sufficient conditions for a protocol to be on the Privacy Frontier and devise alternative protocols on the Privacy Frontier for first-price auctions that allow the designer to flexibly trade off between privacy from bidders and the auctioneer.

Abstract

In many auctions, bidders may be reluctant to reveal private information to the auctioneer and other bidders. Among deterministic bilateral communication protocols, reducing what bidders learn requires increasing what the auctioneer learns. A protocol implementing a given social choice rule is on the Privacy Frontier if no alternative protocol reveals less to both bidders and the auctioneer. For first-price auctions, the descending protocol and the sealed-bid protocol are both on the Privacy Frontier. For second-price auctions, the ascending protocol and the ascending-join protocol of Haupt and Hitzig (2025) are both on the Privacy Frontier, but the sealed-bid protocol is not. We provide sufficient conditions for a protocol to be on the Privacy Frontier and devise alternative protocols on the Privacy Frontier for first-price auctions that allow the designer to flexibly trade off between privacy from bidders and the auctioneer.

Private From Whom? Minimal Information Leakage in Auctions

TL;DR

This work provides sufficient conditions for a protocol to be on the Privacy Frontier and devise alternative protocols on the Privacy Frontier for first-price auctions that allow the designer to flexibly trade off between privacy from bidders and the auctioneer.

Abstract

In many auctions, bidders may be reluctant to reveal private information to the auctioneer and other bidders. Among deterministic bilateral communication protocols, reducing what bidders learn requires increasing what the auctioneer learns. A protocol implementing a given social choice rule is on the Privacy Frontier if no alternative protocol reveals less to both bidders and the auctioneer. For first-price auctions, the descending protocol and the sealed-bid protocol are both on the Privacy Frontier. For second-price auctions, the ascending protocol and the ascending-join protocol of Haupt and Hitzig (2025) are both on the Privacy Frontier, but the sealed-bid protocol is not. We provide sufficient conditions for a protocol to be on the Privacy Frontier and devise alternative protocols on the Privacy Frontier for first-price auctions that allow the designer to flexibly trade off between privacy from bidders and the auctioneer.

Paper Structure

This paper contains 12 sections, 23 theorems, 18 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Literature
  3. Model
  4. Privacy
  5. Impossibility Theorem
  6. The Privacy Frontier
  7. First-Price Auctions
  8. Descending Then Sealed-Bid Protocol
  9. Descending-Holdout Protocol
  10. Second-Price Auctions
  11. Sufficient Conditions for the Privacy Frontier
  12. Conclusion

Key Result

Theorem 1

Suppose $\phi$ violates the indistinguishable corners condition for bidder $i$. No protocol $P$ that implements $\phi$ can satisfy both:

Figures (7)

  • Figure 1: Indistinguishable Corners Condition Violation
  • Figure 2: Choice rule for $\phi^{FPA}$
  • Figure 3: Splitting $\phi^{FPA}$
  • Figure 4: Partition induced by descending then sealed-bid protocol
  • Figure 5: Partition induced by descending-holdout protocol
  • ...and 2 more figures

Theorems & Definitions (58)

  • Definition 1: Contextual Privacy
  • Definition 2: Bidder Information Leakage
  • Definition 3
  • Theorem 1: Impossibility
  • Lemma 1
  • Definition 4
  • Definition 5
  • Definition 6: Privacy Domination
  • Definition 7: Privacy Frontier
  • Definition 8
  • ...and 48 more