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Credible, Optimal Auctions via Public Broadcast

Tarun Chitra, Matheus V. X. Ferreira, Kshitij Kulkarni

TL;DR

This work designs credible, strategyproof auctions in a model that differs from the traditional mechanism design framework because communication is not centralized via the auctioneer, and constructs the first two-round auction that is credible, strategyproof, and optimal when bidder valuations are $\alpha$-strongly regular, for $\alpha>0$.

Abstract

We study auction design in a setting where agents can communicate over a censorship-resistant broadcast channel like the ones we can implement over a public blockchain. We seek to design credible, strategyproof auctions in a model that differs from the traditional mechanism design framework because communication is not centralized via the auctioneer. We prove this allows us to design a larger class of credible auctions where the auctioneer has no incentive to be strategic. Intuitively, a decentralized communication model weakens the auctioneer's adversarial capabilities because they can only inject messages into the communication channel but not delete, delay, or modify the messages from legitimate buyers. Our main result is a separation in the following sense: we give the first instance of an auction that is credible only if communication is decentralized. Moreover, we construct the first two-round auction that is credible, strategyproof, and optimal when bidder valuations are $α$-strongly regular, for $α> 0$. Our result relies on mild assumptions -- namely, the existence of a broadcast channel and cryptographic commitments.

Credible, Optimal Auctions via Public Broadcast

TL;DR

This work designs credible, strategyproof auctions in a model that differs from the traditional mechanism design framework because communication is not centralized via the auctioneer, and constructs the first two-round auction that is credible, strategyproof, and optimal when bidder valuations are -strongly regular, for .

Abstract

We study auction design in a setting where agents can communicate over a censorship-resistant broadcast channel like the ones we can implement over a public blockchain. We seek to design credible, strategyproof auctions in a model that differs from the traditional mechanism design framework because communication is not centralized via the auctioneer. We prove this allows us to design a larger class of credible auctions where the auctioneer has no incentive to be strategic. Intuitively, a decentralized communication model weakens the auctioneer's adversarial capabilities because they can only inject messages into the communication channel but not delete, delay, or modify the messages from legitimate buyers. Our main result is a separation in the following sense: we give the first instance of an auction that is credible only if communication is decentralized. Moreover, we construct the first two-round auction that is credible, strategyproof, and optimal when bidder valuations are -strongly regular, for . Our result relies on mild assumptions -- namely, the existence of a broadcast channel and cryptographic commitments.
Paper Structure (16 sections, 17 theorems, 16 equations)

This paper contains 16 sections, 17 theorems, 16 equations.

Table of Contents

  1. Introduction
  2. Related Work
  3. Technical overview
  4. Paper organization
  5. Preliminaries
  6. Virtual values
  7. Deferred Revelation Auction (DRA) with Public Broadcast
  8. Commitment phase ($1^{st}$ round):
  9. Revelation phase ($2^{nd}$ round):
  10. Resolution phase:
  11. Tie-breaking:
  12. DRA with Public Broadcast is Credible for $\alpha$-Strongly Regular Distributions
  13. Public Broadcast is Necessary
  14. DRA over Public Broadcast for Regular Distributions
  15. Conclusion
  16. ...and 1 more sections

Key Result

Theorem 2.1

Consider a strategyproof auction that awards the item to buyer $i$ with probability $x_i(\vec{v})$ and charges $p_i(\vec{v})$ on bids $\vec{v}$. Then, the expected revenue is We refer to the right-hand side as the expected virtual welfare. For cases where $D$ is regular, $\varphi$ is non-decreasing, and the optimal auction maximizes expected virtual welfare.

Theorems & Definitions (40)

  • Example 1.1
  • Definition 2.1: Ex-post Nash/Strategyproof/Individually Rational
  • Definition 2.2: Credible Auction
  • Theorem 2.1: Myerson's Theorem myerson1981optimal
  • Definition 3.1: Commitment Scheme
  • Definition 3.2: Deferred Revelation Auction with Public Broadcast
  • Theorem 3.1
  • proof
  • Definition 3.3: Centralized Deferred Revelation Auction
  • Lemma 3.1
  • ...and 30 more