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In this paper, we provide a new theoretical framework of pyramid Markovprocesses to solve some open and fundamental problems of blockchain selfishmining under a rigorous mathematical setting. We first describe a more generalmodel of blockchain selfish mining with both a two-block leading competitivecriterion and a new economic incentive mechanism. Then we establish a pyramidMarkov process and show that it is irreducible and positive recurrent, and itsstationary probability vector is matrix-geometric with an explicitlyrepresentable rate matrix. Also, we use the stationary probability vector tostudy the influence of many orphan blocks on the waste of computing resource.Next, we set up a pyramid Markov reward process to investigate the long-runaverage profits of the honest and dishonest mining pools, respectively. As aby-product, we build three approximative Markov processes and provide some newinteresting interpretation on the Markov chain and the revenue analysisreported in the seminal work by Eyal and Sirer (2014). Note that the pyramidMarkov (reward) processes can open up a new avenue in the study of blockchainselfish mining. Thus we hope that the methodology and results developed in thispaper shed light on the blockchain selfish mining such that a series ofpromising research can be developed potentially.

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