Selfish Mining and Dyck Words in Bitcoin and Ethereum Networks

Authors Cyril Grunspan, Ricardo Pérez-Marco

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Author Details

Cyril Grunspan
  • Léonard de Vinci, Research Center, Paris - La Défense, France
Ricardo Pérez-Marco
  • CNRS, IMJ-PRG, Univ. Paris 7, Paris, France

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Cyril Grunspan and Ricardo Pérez-Marco. Selfish Mining and Dyck Words in Bitcoin and Ethereum Networks. In International Conference on Blockchain Economics, Security and Protocols (Tokenomics 2019). Open Access Series in Informatics (OASIcs), Volume 71, pp. 11:1-11:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


The main goal of this article is to present a direct approach for the formula giving the long-term apparent hashrates of Selfish Mining strategies using only elementary probabilities and combinatorics, more precisely, Dyck words. We can avoid computing stationary probabilities on Markov chain, nor stopping times for Poisson processes as in previous analysis. We do apply these techniques to other bockwithholding strategies in Bitcoin, and then, we consider also selfish mining in Ethereum.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Markov processes
  • Bitcoin
  • Blockchain
  • Ethereum
  • Proof-of-Work
  • Selfish Mining
  • Stubborn Mining
  • Apparent Hashrate
  • Revenue Ratio
  • Catalan Distributions
  • Dyck Words
  • Random Walk


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