关键词: 激励机制, 区块链, 马尔可夫链, 合谋攻击, 平稳分布

Abstract: This paper investigates the process by which multiple low-computing-power nodes in a blockchain network collude to exploit incentive mechanisms for excessive gains, comparing node profits under different attack strategies. First, aiming to maximize profits, we construct an optimal strategy combination for joint node attacks and establish a corresponding Markov chain model. We prove the irreducible and normal return properties of this Markov chain, thereby demonstrating the existence of its steady-state distribution. The steady-state distribution is derived by solving the transition rate matrix. Block final states are categorized into 15 types, and transition probabilities between states are analyzed to calculate the occurrence probabilities of each state. Based on this, a long-term node profit model is established. Furthermore, a real blockchain simulation environment is constructed to simulate attack strategies, validating the theoretical findings. Simultaneously, by controlling different variables in the strategy, the block production efficiency and overall profit differences under three scenarios--solo attacks, node defection, and full collusion--are compared and analyzed. The results indicate that some existing blockchain incentive mechanisms still have significant flaws. Nodes with low computing power can substantially increase their profits through collusive manipulation, thereby threatening the fairness and security of the system.

Key words: Incentive mechanism, Blockchain, Markov chain, Collusion attack, Stationary distribution