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

作     者：Quanlin Li Yanxia Chang Xiaole Wu Guoqing Zhang Quanlin Li;Yanxia Chang;Xiaole Wu;Guoqing Zhang

作者机构：School of Economics and ManagementBeijing University of TechnologyBeijing 100124China School of ManagementFudan UniversityShanghai 200433China Department of MechanicalAutomotive&Materials EngineeringUniversity of WindsorWindsorOntarioCanada 

出 版 物：《Journal of Systems Science and Systems Engineering》 (系统科学与系统工程学报（英文版）)

年 卷 期：2021年第30卷第6期

页      面：667-711页

核心收录：

学科分类：081203[工学-计算机应用技术] 08[工学] 0835[工学-软件工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

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 

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

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 *** first describe a more general model of blockchain selfish mining with both a two-block leading competitive criterion and a new economic incentive *** 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 ***,we use the stationary probability vector to study the influence of orphan blocks on the waste of computing ***,we set up a pyramid Markov reward process to investigate the long-run average mining profits of the honest and dishonest mining pools,*** 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 *** 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.