Analysing the Benefit of Selfish Mining with Multiple Players

Many current mainstream blockchain systems, including Bitcoin, adopt Proof-of-Work (PoW) as their consensus protocol. Such a system faces various cryptoeconomic attacks, such as selfish mining. Previous studies have shown that with over 25% of the overall mining power, a selfish miner can benefit by gaining a proportion of rewards higher than its mining power in Bitcoin. This threshold is still higher than any current mining pool, and hence, selfish mining is not considered likely in Bitcoin. Unfortunately, this threshold is only applicable for a single attacker scenario, whereas in a realistic setting, multiple mining pools with significant hash power could perform selfish mining simultaneously. In this paper, we address this research gap by analyzing selfish mining scenarios with multiple independent attackers. Through extensive simulation studies, we show that when the number of selfish miners increases, each of them requires less mining power to gain an advantage, but that the range of mining power such that each selfish miner benefits becomes narrower and thus less sustainable. Our work is the first to show that in practice, there are scenarios where it is enough to have 12% mining power to benefit from selfish mining but also that having more than 7 selfish miners which benefit simultaneously is highly unlikely. We also infer that it is always beneficial for selfish miners to collude and build a more powerful mining pool than to mine independently. Additionally, we propose a safe limit for the size of mining pools in Bitcoin to avoid multi-player attacks. Finally, we extend our studies to Ethereum which uses a different reward model based on uncle blocks.