Model-based Analysis of Mining Fairness in a Blockchain

Mining fairness in blockchain refers to the equality between the computational resources invested in mining and the block rewards received. There exists a dilemma where increasing the blockchain's transaction processing capacity damages mining fairness, consequently undermining its decentralization. This dilemma remains unresolved even with methods such as GHOST, indicating that mining fairness is an inherent bottleneck to the system's transaction processing capacity. Despite its significance, there have been insufficient studies quantitatively analyzing mining fairness. In this paper, we propose a method to calculate mining fairness. Initially, we approximate a complex blockchain network using a simple mathematical model, assuming that no more than two blocks are generated per round. Within this model, we quantitatively determine local mining fairness and derive several measures of global mining fairness based on local mining fairness. We validated that our calculation method accurately computes mining fairness in networks with a small number of miners. Furthermore, we analyzed various networks from the perspective of mining fairness.