Stochastic Modelling of Selfish Mining in Proof-of-Work Protocols

In blockchain-based systems whose consensus mechanisms resort to Proof-of-Work (PoW), it is expected that a miner's share of total block revenue is proportional to their share of hashing power with respect to the rest of the network. The protocol relies on the immediate broadcast of blocks by miners, to earn precedence in peers' local blockchains. However, a deviation from this strategy named selfish mining (SM), may lead miners to earn more than their "fair share". In this paper, we introduce an agent-based model to simulate the dynamics of SM behaviour by a single miner as well as mining pools to understand the influence of (a) mining power distribution, (b) overlay network topology, (c) positioning of the selfish nodes within the peer to peer network. Our minimalistic model allows us to find that in high levels of latency, SM is always a more profitable strategy; our results are very robust to different network topologies and mining nodes' centrality in the network. Moreover, the power-law distribution of the miners' hashing power can make it harder for a selfish miner to be profitable. In addition, we analyze the effect of SM on system global efficiency and fairness. Our analysis confirms that SM is always more profitable for hashing powers representing more than one-third of the total computing power. Further, it also confirms that SM behaviour could cause a statistically significant high probability of continuously mined blocks opening the door for empirical verification of the phenomenon.