Selfish mining is an attack on the integrity of a blockchain network. Inspired by J. Göbel’s selfish mining model in the presence of propagation delay, we propose a competition model based on spatial Poisson process to study how delay influences the revenue distribution when there are more than one selfish miners. Based on our model, we derive the exact expression of the revenue distribution, and prove that the difference of propagation delays between two selfish miners significantly affects the distribution of mining rewards. Additionally, we find that the required threshold of the mining power for multiple selfish miners is larger than that for a single one. Finally, we discuss how the propagation delay impacts the state transfer machine of each selfish miner.

自私的挖矿是对区块链网络完整性的攻击。受J.Göbel在存在传播延迟的情况下自私采矿模型的启发，我们提出了一种基于空间泊松过程的竞争模型，以研究存在多个自私矿工时延迟对收入分配的影响。基于我们的模型，我们得出收入分配的精确表达式，并证明两个自私的矿工之间的传播延迟差异显着影响了采矿奖励的分布。此外，我们发现多个自私矿工所需的采矿权门槛要比单个矿工更大。最后，我们讨论传播延迟如何影响每个自私矿工的状态转移机器。