Cooperation And Optimization Of Mining Pool Game Based On PoW Consensus Algorithm

Blockchain technology,also known as distributed ledger technology,has the characteristics of decentralization,openness and transparency.Since everyone can participate in database records,blockchain technology has very promising application prospects in various industries,and has received more and more attentions.Solving the SHA256problem(also known as mining)is a key issue in the Proof of Work(PoW)consensus algorithm.Because it is difficult to obtain revenue by mining alone,miners generally choose to join the mining pools.However,block withholding attack will carry out among the pools to pursue their own profits,which leads to a decline of system revenue.The mining pool dilemma in the PoW consensus process corresponds to the classic prisoner dilemma model,and its Nash equilibrium is mutual attack.However,when the mining pools attack each other,the benefits are less than when there is no attack,that is,the system is not optimal.In order to improve the system revenue,it is necessary to establish relevant mechanisms and optimize the strategy selection of the mining pool game.Firstly,based on PoW consensus,the paper takes the dual-pool mining game as an example to establish a dual-pool dual-strategy game model and analyzes its pure strategy Nash equilibrium and mixed strategy Nash equilibrium.For mixed strategy Nash equilibrium,the existence conditions of equilibrium are given,and two important inferences are obtained.In order to improve the system income,a zero determinant strategy algorithm is introduced.It is found that the mining pool using this strategy can control the income of the other mining pool to have a linear relationship with itself,thereby controlling the overall system income,so that the mining pools tend to cooperate to obtain higher system benefits.Secondly,although the use of the ZD strategy by individual mining pools can optimize system revenue,when the number of mining pools in the blockchain network is large,the system revenue optimization effect cannot reach a stable optimal state.Therefore,we consider combining the mining pool with the ZD strategy for alliance.According to different communication levels,two ZD alliance strategies are applied,namely ”strategic alliance” and ”synchronous alliance”.Through the exploration,it is found that the more mining pools there are in the alliance,the higher the system revenue value is.Finally,the paper considers that in a mining pool,miners can perform block with-holding attacks on the mining pool and share the benefits of the mining pool with other miners.However,block withholding attacks also exist between mining pools.Mining pools use miners to infiltrate into other mining pools and conduct block withholding attacks on other mining pools to obtain revenue in order to increase the total revenue of their own mining pools.And,there will be a situation where miners who infiltrate into other mining pools will betray,that is,the miners faithfully mine in the mining pool and do not bring the revenue back to the original mining pool.Based on these situations,the paper conductes an in-depth and specific analysis.The infiltrate rate and betrayal rate of the mining pool are considered in models.The Nash equilibrium and the value of the infiltration rate when the mining pool game is optimized under different computing power are analyzed.And the influence of the mining pool’s computing power,the ratio of the power to be infiltrated,and the betrayed rate of dispatched miners on the mining pool’s infiltration rate selection and income are explored.