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arXiv · 2607.24415

Near-Tight Theoretical Bounds for Incentive Compatibility in Bitcoin Mining

Akira Sakurai·Taishi Nakai·Kazuyuki Shudo
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Abstract

When is honest Bitcoin mining rational? This question is central to the incentive design of proof-of-work blockchains. Sapirshtein et al. computationally derived near-tight lower and upper bounds on the incentive-compatibility threshold using a Markov Decision Process. Kiayias et al.'s Blockchain Mining Games instead derived theoretical lower and upper bounds. However, this theoretical approach has two limitations: its model restricts miners to a narrow action space and assumes idealized tie behavior, and its lower and upper bounds are far from tight. We resolve both limitations. We develop a more realistic model with a broader miner action space and asymmetric tie-breaking parameters $\gamma^-$ and $\gamma^+$. We then propose an algorithm that computes lower and upper bounds on the incentive-compatibility threshold with a maximum error of $9.98006\times10^{-4}$.

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Akira Sakurai, Taishi Nakai, Kazuyuki Shudo. 2026-07-27. Near-Tight Theoretical Bounds for Incentive Compatibility in Bitcoin Mining. https://arxiv.org/abs/2607.24415

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