Characterizing Off-Chain Influence Proof Transaction Fee Mechanisms

TL;DR

This paper characterizes off-chain influence-proof transaction fee mechanisms, showing their relation to burn identities and virtual values, and explores their existence beyond cryptographic methods in various settings.

Contribution

It provides a comprehensive characterization of OffCIP TFMs using burn identities and virtual values, extending understanding beyond cryptographic mechanisms.

Findings

OffCIP TFMs satisfy a burn identity relating burn and allocation rules.

Deterministic OffCIP and OnCS TFMs without cryptography are posted-price mechanisms with special burns.

Randomized OffCIP and OnCS TFMs exist even with finite supply and prior dependence.

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.