# Stochastic Modelling of Selfish Mining in Proof-of-Work Protocols +
## 7 Discussion and Conclusions  
In this paper, we introduced an agent-based model that simulates the selfish mining strategy in a Proof-of-Work protocol setting. The modelling of a peer-to-peer network structure allows us to extensively study the effects of block propagation delays, network topology and mining power distribution on relative selfish revenue. After simulating the selfish miner's behaviour, we further analyze the influence of selfish mining on network efficiency and reward fairness using orphan block rate and Gini index respectively.Our research suggests that selfish mining is a viable and profitable strategy. Assuming a single selfish miner, we show that relative selfish revenue is a decreasing function of block propagation speed. Further, we find that for high levels of latency selfish  
Figure 10: Single realisations for a selfish mining pool: Share of main chain blocks as a function of the share of hashing power for all nodes. In subfigures (**a**,**b**), all selfish miners in the mining pool control 20% hashing power, and in (**c**,**d**) those selfish miners control 40% hashing power. In addition, the subfigures in left column show the results when network has high latency \(\lambda_{nd}=0.63\), and subfigures in right column show the results with low network latency \(\lambda_{nd}=7.14\). mining is always a relatively more profitable strategy. In particular, we confirm [2]'s main observation that selfish mining is always relatively more profitable for hashing power share being more than 1/3, even when considering network dynamics such as latency. Furthermore, we show that the dynamics of selfish mining are very robust to changes in the underlying network topology and the centrality of the selfish miner's location. However, we find that a hashing power distribution following a power law greatly affects relative selfish revenue. In other words, powerful honest nodes can make it harder for selfish miners to be relatively more profitable. Regarding the global effect, we find that when selfish mining is relatively more profitable, the block reward concentration also increases. Besides the intuition that slower block diffusion would cause a high rate of orphan blocks, we also reveal that with the selfish miner's share of the network's hashing power increasing to 50%, the orphan block rate also converges towards 50% and the main chain no-sibling rate converges to 100%. Finally, using Miner Sequence Bootstrapping (MSB) index [24, 25], we confirm selfish mining behaviour also causes statistically significant levels of consecutive blocks by the same miner, which is beneficial in detecting selfish miners in real-world systems such as Bitcoin. The composability of our ABM has the advantage of allowing modifications to the behaviour of agents easily. In addition, the model is flexible to simulate more selfish miners too. We extend the model to analyse the dynamic when multiple selfish miners cooperate within a pool. For the simplification, we currently assume that the communication within the mining pool and outside the pool follows the same rate. However, in reality, it is more likely that pool members use more efficient means of communication. For example, rather than propagating entire blocks only sending block headers might decrease latency. Thus, an improvement to the model would consider faster in-pool communication than the average information propagation time among the network. Another limitation is that some of our simulations were limited by the relatively small network size, which may cause a lack of heterogeneity in the network [15]. An extension of this work will include larger networks as well as non-mining full nodes as part of the peer-to-peer network. Further, the effect of the selfish miner's network location, as well as their connectivity, will be considered. For example, we are planning to propose a new concept of _lashing centrality_ in the peer-to-peer mining network, to study the effect of selfish miners being connected to \"powerful\" honest nodes.