Selfish mining strategy elaboration | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2020. № 49. DOI: 10.17223/20710410/49/5

As it was shown by Ittay Eyal and Emin Gun Sirer, the Bitcoin mining protocol is not incentive-compatible, because there exists an attack in which colluding miners obtain a revenue larger than their fair share. We describe an elaboration of Selfish-Mine Strategy and present an extended model of selfish mining based on independency hypothesis: both groups are made their work independently from each other. We describe a new state machine modelling selfish pool strategy. Let the selfish pool has mining power of р, 0 <р< 1/2, and the others of (1 - р). We also consider the situation in which the others mine a block on the previously private branch (frequency γ(1 - р)), and the others mine a block on the public branch (frequency (1 - γ)(1 - р)). Main result is an elaboration of an interval in which selfish miners will earn more than their relative mining power: 1) for a given р, a pool of size р obtains a revenue larger than than its relative size for p in the following range: 0 < p ≤ 0.429 (the left bound corresponds to 7 = 1, and the right one - to 7 = 0); 2) for a given p, a pool of size p obtains a revenue larger than a revenue of other group in the following range: 0.358 ≤ p ≤ 0.449.