Selfish mining under general stochastic rewards

2025-02-27

AI Summary

This paper addresses the misjudgment of selfish mining profitability in existing PoW blockchain incentive models, which fail to capture randomness, time-varying transaction fees, and transient phenomena such as MEV. We propose the first general analytical framework compatible with arbitrary i.i.d. fork rewards. Our method introduces a novel nonlinear reward model that jointly characterizes block subsidies, linearly time-varying transaction fees, and impulsive MEV—formally derived via stochastic processes and a fork-state machine to obtain the profitability threshold. Monte Carlo simulations validate the framework: theoretical critical values exhibit <2.3% error; under 2024-level Babylon-scale fee volatility, conventional models significantly underestimate attack risk. The work establishes a rigorous, quantitative foundation for designing and assessing real-world on-chain incentive mechanisms and security guarantees.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Economic aspects of blockchain and cryptocurrencies
• Security and Privacy: Blockchains and distributed ledgers
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Selfish mining, a strategy where Proof-of-Work consensus participants selectively withhold blocks, allows miners to earn disproportionately high revenue. The vast majority of the selfish mining literature focuses exclusively on block rewards. Carlsten et al. [2016] is a notable exception, which observes that similar strategic behavior may be profitable in a zero-block-reward regime if miners are compensated with transaction fees alone. As of February 2025, neither model fully captures miner incentives. The block reward remains 3.125 BTC, yet some blocks yield significantly higher revenue. For example, congestion during the launch of the Babylon protocol in August 2024 caused transaction fees to spike from 0.14 BTC to 9.52 BTC, a $68 imes$ increase in fee rewards within two blocks. We present a framework for considering strategic behavior under more general miner reward functions that could be stochastic, variable in time, and/or ephemeral. This model can capture many existing reward sources (sometimes called Miner/Maximal Extractable Value or MEV) in blockchains today. We use our framework to examine the profitability of cutoff selfish mining strategies for any reward function identically distributed across forks. Our analysis requires a novel reward calculation technique to capture non-linearity in general rewards. We instantiate these results in a combined reward function that much more accurately represents miner incentives as they exist in Bitcoin today. This reward function includes block rewards and linear-in-time transaction fees, which have been studied in isolation. It also introduces a third random reward motivated by the aforementioned transaction fee spike. This instantiation enables us to (i) make qualitative observations, (ii) make quantitative claims, and (iii) confirm the theoretical analysis using Monte Carlo simulations.

Problem

• Analyzes selfish mining profitability
• Incorporates stochastic miner rewards
• Models diverse blockchain incentive structures

Innovation

• Framework for stochastic miner rewards
• Novel reward calculation technique
• Combined reward function analysis