关键词: 激励机制, 区块链, 马尔可夫模型, 正递归, 平稳分布

Abstract: In this paper, we mainly study the process of small computing power nodes in Blockchain making profits by jointly using the defects of incentive mechanism and the comparison of benefits under different strategies. Firstly, we formulated the optimal combination strategy based on the principle of income maximization, established the Markov chain model, proved the irreducibility and positive recursion of the Markov process, and further proved the existence of its stationary distribution. Then, by solving the stationary distribution of the process through its Q matrix, we divided the final state of the block into 15 types of analysis, calculated the possibility of the final state of the block by analyzing the transformation probability between States, and then established a long-term income model. On this basis, we built a real blockchain environment, simulated the strategy and compared it with the theory; At the same time, by separately controlling different variables in the strategy, we analyzed the blocking speed and overall income of the three strategies of individual, betrayal and combination, and obtained the advantages and disadvantages of their respective strategies, indicating that Blockchain's current incentive mechanism still has great defects, which is easy to be used by small computing nodes and joint game operation to make profits.

Key words: Excitation mechanism, Blockchain , Markov model , Positive recurrent, Invariant distribution