# Selfish Mining in Proof-of-Work Blockchain with Multiple Miners: An Empirical Evaluation

## TL;DR

This paper empirically evaluates the impact of selfish mining in proof-of-work blockchains with multiple miners, revealing how the number and behavior of miners influence system robustness and mining rewards.

## Contribution

It provides the first empirical analysis of selfish mining with multiple malicious and strategic miners, highlighting effects on rewards and system stability.

## Key findings

- Selfish mining becomes more effective with more SM miners.
- Presence of strategic miners does not significantly affect SM effectiveness.
- Increasing strategic miners enhances blockchain robustness.

## Abstract

Proof-of-Work blockchain, despite its numerous benefits, is still not an entirely secure technology due to the existence of Selfish Mining (SM) strategies that can disrupt the system and its mining economy. While the effect of SM has been studied mostly in a two-miners scenario, it has not been investigated in a more practical context where there are multiple malicious miners individually performing SM. To fill this gap, we carry out an empirical study that separately accounts for different numbers of SM miners (who always perform SM) and strategic miners (who choose either SM or Nakamoto's mining protocol depending on which maximises their individual mining reward). Our result shows that SM is generally more effective as the number of SM miners increases, however its effectiveness does not vary in the presence of a large number of strategic miners. Under specific mining power distributions, we also demonstrate that multiple miners can perform SM and simultaneously gain higher mining rewards than they should. Surprisingly, we also show that the more strategic miners there are, the more robust the systems become. Since blockchain miners should naturally be seen as self-interested strategic miners, our findings encourage blockchain system developers and engineers to attract as many miners as possible to prevent SM and similar behaviour.