Propagation Delay and Mining Centralization: Modeling Stale Rates

The detailed analysis focuses on the concept of "Selfish Mining", a strategy that allows miners to increase their revenues by selectively publishing blocks. This strategy, under certain conditions, can give larger miners an advantage through longer block propagation times. The core of the analysis is based on a simplified model to understand how block propagation time can affect a miner's revenue in relation to its hashrate. It assumes uniform propagation time and a scenario where all miners immediately start mining upon finding a block, publish it instantly, and switch to a valid chain with more proof of work as soon as it's received, essentially forming a star network topology within the Bitcoin peer-to-peer network.

In conditions where propagation time is instant, a miner's revenue would be directly proportional to its share of the network's hashrate. However, due to non-instant propagation, there's always a risk of a miner's block becoming stale if another miner's competing block is propagated first and wins the race. The analysis breaks down into two scenarios: one where another miner finds a block before the miner in question does, leading to all other miners working off the competing block, and another scenario where a block is found shortly after, which increases the chance of the original block becoming stale if the same miner or another finds a subsequent block quickly.

The probability of a block going stale depends significantly on the miner's control over the network's hashrate, with centralization playing a crucial role. Larger miners or pools have a higher chance of winning these races, demonstrating how block propagation times can inadvertently encourage mining centralization. Simulations based on hashrate distributions from the past three months provide insight into how different propagation times affect the stale rate and, consequently, the net benefit for various pools. Even slight differences in propagation times can lead to significant shifts in revenue, highlighting the importance of choosing the right pool based on size and the potential impact of changes to the P2P network on mining dynamics.

This analysis underscores the intricate balance between block propagation times, miner strategies, and the overall fairness and decentralization of the mining process. It suggests that improvements in the P2P network that reduce propagation delays could make mining more equitable across differently sized operations, potentially mitigating some aspects of centralization. The findings are supported by data visualizations and simulation results, available through provided links such as the detailed analysis of Selfish Mining and the source code for the simulations at GitHub, offering a deeper dive into the technicalities and numerical implications of the study.