Rewarding miners: bankruptcy situations and pooling strategies

In Proof-of-Work (PoW) based blockchains (e.g., Bitcoin), mining is the procedure through which miners can gain money on regular basis by finding solutions to a mathematical crypto puzzle (i.e., full solutions) which validates blockchain transactions. In order to reduce the uncertainty of the remuneration over time, miners cooperate and form pools. Each pool receives a reward which has to be split among pool's participants. The objective of this paper is to find an allocation method, for a mining pool, aimed at redistributing the reward among cooperating miners and, at the same time, preventing some malicious behaviours of the miners. Recently, Schrijvers et al. (2017) have proposed an allocation method that is incentive compatible , ensuring that miners have an advantage to report full solutions to the pool immediately. However, such a method encourages an harmful inter-pool behaviour (i.e., pool hopping) when the reward results insufficient to remunerate pool miners, determining a loss in terms of pool's computational power. By reinterpreting the allocation rules as outcomes of bankruptcy situations, we define a new reward function based on the well-studied Constrained Equal Losses (CEL) rule that maintains the incentive compatible property while making pool hopping less advantageous.