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Characterizing Off-Chain Influence Proof Transaction Fee Mechanisms

Aadityan Ganesh, Clayton Thomas, S. Matthew Weinberg

TL;DR

<3-5 sentence high-level summary>

Abstract

Roughgarden (2020) initiates the study of Transaction Fee Mechanisms (TFMs), and posits that the on-chain game of a ``good'' TFM should be on-chain simple (OnCS), i.e., incentive compatible for users and the miner. Recent work of Ganesh, Thomas and Weinberg (2024) posits that they should additionally be Off-Chain Influence Proof (OffCIP), which means that the miner cannot achieve any additional revenue by separately conducting an off-chain auction to determine on-chain inclusion. They observe that a cryptographic second-price auction satisfies both properties, but leave open the question of whether other mechanisms (e.g, non-cryptographic) satisfy these properties. In this paper, we characterize OffCIP TFMs: They are those satisfying a burn identity relating the burn rule to the allocation rule. In particular, we show that auction is OffCIP if and only if its (induced direct-revelation) allocation rule $\bar{X}(\cdot)$ and burn rule $\bar{B}(\cdot)$ (both of which take as input users' values $v_1, \dots, v_n$) are truthful when viewing $\big(\bar{X}(\cdot), \bar{B}(\cdot)\big)$ as the allocation and pricing rule of a multi-item auction for a single additive buyer with values $\big(\varphi(v_1),\ldots, \varphi(v_n)\big)$ equal to the users' virtual values. Building on this burn identity, we characterize deterministic OffCIP and OnCS TFMs that do not use cryptography: They are posted-price mechanisms with specially-tuned burns. As a corollary, we show that such TFMs can only exist with infinite supply and prior-dependence. However, we show that for randomized TFMs, there are additional OnCS and OffCIP auctions that do not use cryptography (even when there is finite supply, under prior-dependence with a bounded prior distribution). Holistically, our results show that while OffCIP is a fairly stringent requirement, families of OffCIP mechanisms can be found for a variety of settings.

Characterizing Off-Chain Influence Proof Transaction Fee Mechanisms

TL;DR

<3-5 sentence high-level summary>

Abstract

Roughgarden (2020) initiates the study of Transaction Fee Mechanisms (TFMs), and posits that the on-chain game of a ``good'' TFM should be on-chain simple (OnCS), i.e., incentive compatible for users and the miner. Recent work of Ganesh, Thomas and Weinberg (2024) posits that they should additionally be Off-Chain Influence Proof (OffCIP), which means that the miner cannot achieve any additional revenue by separately conducting an off-chain auction to determine on-chain inclusion. They observe that a cryptographic second-price auction satisfies both properties, but leave open the question of whether other mechanisms (e.g, non-cryptographic) satisfy these properties. In this paper, we characterize OffCIP TFMs: They are those satisfying a burn identity relating the burn rule to the allocation rule. In particular, we show that auction is OffCIP if and only if its (induced direct-revelation) allocation rule and burn rule (both of which take as input users' values ) are truthful when viewing as the allocation and pricing rule of a multi-item auction for a single additive buyer with values equal to the users' virtual values. Building on this burn identity, we characterize deterministic OffCIP and OnCS TFMs that do not use cryptography: They are posted-price mechanisms with specially-tuned burns. As a corollary, we show that such TFMs can only exist with infinite supply and prior-dependence. However, we show that for randomized TFMs, there are additional OnCS and OffCIP auctions that do not use cryptography (even when there is finite supply, under prior-dependence with a bounded prior distribution). Holistically, our results show that while OffCIP is a fairly stringent requirement, families of OffCIP mechanisms can be found for a variety of settings.

Paper Structure

This paper contains 47 sections, 32 theorems, 120 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. TFM Design Thus-Far.
  3. Related Work
  4. Road-map
  5. Preliminaries: Model of Transaction Fee Mechanisms
  6. Warmup: Characterizing Off-Chain Influence Proof Posted-Price Mechanisms
  7. Myerson-in-Range Mechanisms and a Multi-Item Monopsonist Lens
  8. Myerson-in-Range Mechanisms and Off-Chain Influence Proofness
  9. Three Canonical Properties of Myerson-in-Range Mechanisms
  10. The Burn Identity for Myerson-in-Range Mechanisms
  11. Prior-Independent On-Chain Miner Simple and Off-Chain Influence Proof Mechanisms Require Both Cryptography and Miner Advice
  12. Prior-Dependent, On-Chain User and Miner Simple, Off-Chain Influence Proof, Plain-Text Mechanisms
  13. A Sufficient Condition for Prior-Dependent On-Chain User Simple and Off-Chain Influence Proof Mechanisms
  14. Deterministic Simple-to-Participate Mechanisms
  15. Position Auctions with Burn
  16. ...and 32 more sections

Key Result

proposition 3.1

For a distribution $\mathcal{T}$ of user values with a continuous virtual value function $\varphi$, suppose that the block-building process posts a price $Q$ and burns $B$ per allocated user. Then, the equilibrium $\sigma^{\mathcal{C}}_{\mathsf{honest}}$ is off-chain influence proof if and only if $

Figures (3)

  • Figure 1: Main arguments used to prove \ref{['thm:NoDeterministicMechanisms']}.
  • Figure 2: The allocation rule of a TFM supporting at most $2$ bids.
  • Figure 3: The allocation rule for user $(i)$ in a position auction with and without a fabricated bid $w$. For a value profile $\vec{v}_{-(i)}$, \ref{['fig:PositionAuctionWithoutw']} denotes the allocation to user $(i)$ as a function of his bid $v$. For $w$ such that $v^{(t+1)} \leq w \leq v^{(t)}$, \ref{['fig:PositionAuctionWithw']} denotes the allocation rule for user $(i)$ after the miner fabricates a bid $w$. Note the change in allocation probabilities when user $(i)$ bids $v \in [\varphi^{-1}(0), v^{(t)}]$.

Theorems & Definitions (70)

  • proposition 3.1
  • proof
  • definition 4.1: Direct-revelation mechanism
  • definition 4.2: Myerson-in-Range
  • lemma 4.3
  • theorem 4.4
  • theorem 4.5
  • theorem 4.6
  • definition 4.7: Monopsonist smoothening
  • theorem 4.8: Rochet85
  • ...and 60 more