The Optimal Mining Strategy of Proof of Stake Consensus in Peercoin Blockchain

The integration of distributed data storage, P2P networks, consensus mechanisms, cryptography and other technologies, the application of blockchain technology has expanded from the initial financial field to many other areas, such as logistics and auditing. The consensus mechanism is the soul of blockchain technology, and it is of great significance to conduct a rigorous mathematical analysis. As far as we know, the Proof of Stake (PoS) consensus mechanism is only a qualitative description of the rich and the poor, the rich are richer, the poor are poorer, and there is no quantitative mathematical analysis. This paper presents a novel quantitative framework to quantitatively analyze the PoS consensus mechanism. Under the premise of not carrying out the attack, we use the expected reward and the reward ratio as the evaluation indicators, quantitatively analyze the optimal fund allocation strategy of the two parties game under the PoS consensus mechanism from the perspective of rich miners, and construct the reward function as the objective function. The inequality constrains the optimization problem and solves it using the Karush-Kuhn-Tucker condition. We consider the two schemes of assignment strategy and random strategy, and get the optimal fund allocation strategy. At the same time, it is compared with the general strategy to obtain the optimization effect of the optimal strategy. After that, we compare the situation in which both sides of the game use the optimal strategy. We found that for assignment strategy, the mining activity will not indicate that the rich are richer and the poor are poorer. However, for the random strategy, this will not happen. The random strategy is also the most common strategy in practice. We also use Markov decision process (MDP) to give the optimal strategy calculation method under the rational miner game, which is also applicable to the n-parties game. The work of this paper helps the blockchain developers to analyze the PoS consensus mechanism, and the adoption strategy of the assignment strategy and the random strategy can be used as the future research direction.