Temporary fork is a fundamental phenomenon in many blockchains with proof of work, and the analysis of temporary fork has recently drawn great attention. Different from existing efforts that focus on the blockchain system factors such as block size, network propagation delay or block generation speed, in this paper we explore a new key dimension of computing power from the miners' perspective. Specifically, we first propose a detailed mathematical model to characterize the impact of computing power competition of the mining pools on the temporary fork. We also derive closed-form formula of the probability of temporary fork and the expected mining reward of a mining pool. To reveal the long-term trends on the computing power distributions over the competing mining pools, we then develop an evolutionary game framework based on the temporary fork modeling and accordingly characterize the set of stable evolution equilibriums. Both extensive numerical simulations and realistic blockchain data based evaluation provide evidence to support our theoretical models and discoveries.

中文翻译：

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临时分叉对区块链网络矿池演化的影响：演化博弈分析

临时分叉是很多有工作量证明的区块链的基本现象，对临时分叉的分析最近备受关注。与现有的工作侧重于区块大小、网络传播延迟或区块生成速度等区块链系统因素不同，本文从矿工的角度探索计算能力的新关键维度。具体来说，我们首先提出了一个详细的数学模型来表征矿池的算力竞争对临时分叉的影响。我们还推导出了临时分叉概率和矿池预期挖矿奖励的闭式公式。为了揭示竞争矿池的计算能力分布的长期趋势，然后，我们基于临时分叉模型开发了一个演化博弈框架，并相应地表征了一组稳定的演化均衡。广泛的数值模拟和基于现实区块链数据的评估都为支持我们的理论模型和发现提供了证据。