A New Theoretical Framework of Pyramid Markov Processes for Blockchain Selfish Mining  

作　　者：Quanlin Li Yanxia Chang Xiaole Wu Guoqing Zhang 

机构地区：[1]School of Economics and Management,Beijing University of Technology,Beijing 100124,China [2]School of Management,Fudan University,Shanghai 200433,China [3]Department of Mechanical,Automotive&Materials Engineering,University of Windsor,Windsor,Ontario,Canada

出　　处：《Journal of Systems Science and Systems Engineering》2021年第6期667-711,共45页系统科学与系统工程学报（英文版）

基　　金：This work is supported by the National Key R&D Program of China under Grant No.2020AAA0103801;Quanlin Li is supported by the National Natural Science Foundation of China under Grant Nos.71671158 and 71932002;the Beijing Social Science Foundation Research Base Project under Grant No.19JDGLA004;Xiaole Wu is supported by the National Natural Science Foundation of China under Grant No.72025102.

摘　　要：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.

关 键 词：Blockchain Proof of Work selfish mining main chain pyramid Markov process pyramid Markov reward process phase-type distribution Matrix-geometric solution 

分 类 号：TP39[自动化与计算机技术—计算机应用技术]