Near-Tight Theoretical Bounds for Incentive Compatibility in Bitcoin Mining

2026-07-27

AI Summary

This study investigates the incentive compatibility conditions under which rational miners in Bitcoin mining choose to follow the honest strategy. To this end, we develop a more realistic mining game model that expands the miners’ action space and incorporates asymmetric tie-breaking parameters, denoted γ⁻ and γ⁺. By integrating game-theoretic analysis with Markov decision processes, an enhanced blockchain mining model, and efficient numerical optimization algorithms, our approach overcomes the limitations of traditional models—specifically their restricted action spaces and idealized tie-breaking assumptions. We compute near-tight upper and lower bounds on the incentive compatibility threshold with a maximum error of 9.98006×10⁻⁴, substantially narrowing the theoretical gap and providing high-precision analytical support for incentive design in Proof-of-Work consensus mechanisms.

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 $γ^-$ and $γ^+$. We then propose an algorithm that computes lower and upper bounds on the incentive-compatibility threshold with a maximum error of $9.98006\times10^{-4}$.

Problem

• incentive compatibility
• Bitcoin mining
• theoretical bounds
• Markov Decision Process
• blockchain mining games

Innovation

• incentive compatibility
• Bitcoin mining
• Markov Decision Process
• asymmetric tie-breaking
• tight bounds