AI 中文总结
研究比特币挖矿中诚实挖矿何时理性的激励设计问题，针对现有理论方法局限性，开发更现实模型及非对称平局决胜参数，提出算法计算激励兼容性阈值上下界，最大误差为9.98006×10⁻⁴。
AI 中文摘要
诚实的比特币挖矿何时是理性的？这个问题是工作量证明区块链激励设计的核心。Sapirshtein等人使用马尔可夫决策过程通过计算得出激励兼容性阈值的近紧上下界。Kiayias等人的区块链挖矿博弈则得出了理论上下界。但该理论方法有两个局限性：模型将矿工限制在狭窄的行动空间并假设理想化的平局行为，且上下界不够紧密。我们解决了这两个局限性。开发了一个更现实的模型，具有更广泛的矿工行动空间和非对称平局决胜参数γ⁻和γ⁺。然后提出一种算法，计算激励兼容性阈值的上下界，最大误差为9.98006×10⁻⁴。
英文摘要
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 $9.98006\times10^{-4}$.
