Transaction fee mechanism for Proof-of-Stake protocol
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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 (γ) proposed in Chung and Shi (where γ is a key parameter in the strict γ-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 (γ) mechanism will fail a key desired property in TFM, c-side contract proofness (c-SCP). As a remedy, we introduce another parameter θ, and propose a new (θ) 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 θ falls into a specific range, along with a proper tick size imposed on user bids.
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