Bitcoin Selfish Mining and Dyck Words
This work offers a more accessible mathematical analysis for researchers studying blockchain security and mining strategies, but it is incremental as it simplifies existing proofs rather than introducing new concepts.
The paper provides a simpler proof for the long-term apparent hashrate of Bitcoin's Selfish Mining strategy using elementary probabilities and Dyck words, eliminating the need for complex Markov chain or Poisson process calculations, and also examines other block withholding strategies.
We give a straightforward proof for the formula giving the long-term apparent hashrate of the Selfish Mining strategy in Bitcoin using only elementary probabilities and combinatorics, and more precisely, Dyck words. There is no need to compute stationary probabilities on Markov chain nor stopping times for Poisson processes as it was previously done. We consider also several other block withholding strategies.