  In blockchain networks adopting the proof-of-work schemes, the monetary
incentive is introduced by the Nakamoto consensus protocol to guide the
behaviors of the full nodes (i.e., block miners) in the process of maintaining
the consensus about the blockchain state. The block miners have to devote their
computation power measured in hash rate in a crypto-puzzle solving competition
to win the reward of publishing (a.k.a., mining) new blocks. Due to the
exponentially increasing difficulty of the crypto-puzzle, individual block
miners tends to join mining pools, i.e., the coalitions of miners, in order to
reduce the income variance and earn stable profits. In this paper, we study the
dynamics of mining pool selection in a blockchain network, where mining pools
may choose arbitrary block mining strategies. We identify the hash rate and the
block propagation delay as two major factors determining the outcomes of mining
competition, and then model the strategy evolution of the individual miners as
an evolutionary game. We provide the theoretical analysis of the evolutionary
stability for the pool selection dynamics in a case study of two mining pools.
The numerical simulations provide the evidence to support our theoretical
discoveries as well as demonstrating the stability in the evolution of miners'
strategies in a general case.
