Characterizing Off-Chain Influence Proof Transaction Fee Mechanisms

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.