In this paper,we provide a new theoretical framework of pyramid Markov processes to solve some open and fundamental problems of blockchain selfish mining under a rigorous mathematical setting.We first describe a more ...In this paper,we provide a new theoretical framework of pyramid Markov processes to solve some open and fundamental problems of blockchain selfish mining under a rigorous mathematical setting.We first describe a more general model of blockchain selfish mining with both a two-block leading competitive criterion and a new economic incentive mechanism.Then we establish a pyramid Markov process and show that it is irreducible and positive recurrent,and its stationary probability vector is matrix-geometric with an explicitly representable rate matrix.Also,we use the stationary probability vector to study the influence of orphan blocks on the waste of computing resource.Next,we set up a pyramid Markov reward process to investigate the long-run average mining profits of the honest and dishonest mining pools,respectively.As a by-product,we build one-dimensional Markov reward processes and provide some new interesting interpretation on the Markov chain and the revenue analysis reported in the seminal work by Eyal and Sirer(2014).Note that the pyramid Markov(reward)processes can open up a new avenue in the study of blockchain selfish mining.Thus we hope that the methodology and results developed in this paper shed light on the blockchain selfish mining such that a series of promising research can be developed potentially.展开更多
基金This work is supported by the National Key R&D Program of China under Grant No.2020AAA0103801Quanlin Li is supported by the National Natural Science Foundation of China under Grant Nos.71671158 and 71932002+1 种基金the Beijing Social Science Foundation Research Base Project under Grant No.19JDGLA004Xiaole Wu is supported by the National Natural Science Foundation of China under Grant No.72025102.
文摘In this paper,we provide a new theoretical framework of pyramid Markov processes to solve some open and fundamental problems of blockchain selfish mining under a rigorous mathematical setting.We first describe a more general model of blockchain selfish mining with both a two-block leading competitive criterion and a new economic incentive mechanism.Then we establish a pyramid Markov process and show that it is irreducible and positive recurrent,and its stationary probability vector is matrix-geometric with an explicitly representable rate matrix.Also,we use the stationary probability vector to study the influence of orphan blocks on the waste of computing resource.Next,we set up a pyramid Markov reward process to investigate the long-run average mining profits of the honest and dishonest mining pools,respectively.As a by-product,we build one-dimensional Markov reward processes and provide some new interesting interpretation on the Markov chain and the revenue analysis reported in the seminal work by Eyal and Sirer(2014).Note that the pyramid Markov(reward)processes can open up a new avenue in the study of blockchain selfish mining.Thus we hope that the methodology and results developed in this paper shed light on the blockchain selfish mining such that a series of promising research can be developed potentially.
