Transaction fee mechanism for Proof-of-Stake protocol

TL;DR

This paper extends a transaction fee mechanism for proof-of-stake blockchains by incorporating a long-run utility model for miners, revealing a utility discontinuity issue, and proposing a modified mechanism that satisfies key incentive and security properties.

Contribution

It introduces a new utility-based analysis of the BSP mechanism, identifies a critical utility discontinuity, and proposes a modified mechanism with parameters ensuring all desired properties.

Findings

Derived an explicit long-run utility function for miners.

Identified a utility discontinuity causing failure of $c$-SCP.

Proposed a modified BSP mechanism satisfying all incentive and security properties.

Abstract

We study a mechanism design problem in the blockchain proof-of-stake (PoS) protocol. Our main objective is to extend the transaction fee mechanism (TFM) recently proposed in Chung and Shi (SODA, p.3856-3899, 2023), so as to incorporate a long-run utility model for the miner into the burning second-price auction mechanism $\texttt{BSP}(\gamma)$ proposed in Chung and Shi (where $\gamma$ is a key parameter in the strict $\gamma$-utility model that is applied to both miners and users). First, we derive an explicit functional form for the long-run utility of the miner using a martingale approach, and reveal a critical discontinuity of the utility function, namely a small deviation from being truthful will yield a discrete jump (up or down) in the miner's utility. We show that because of this discontinuity the $\texttt{BSP}(\gamma)$ mechanism will fail a key desired property in TFM, $c$-side contract proofness ($c$-SCP). As a remedy, we introduce another parameter $\theta$, and propose a new $\texttt{BSP}(\theta)$ mechanism, and prove that it satisfies all three desired properties of TFM: user- and miner-incentive compatibility (UIC and MIC) as well as $c$-SCP, provided the parameter $\theta$ falls into a specific range, along with a proper tick size imposed on user bids.