Nash Equilibrium of Multiple, Non-Uniform Bitcoin Block Withholding Attackers

Abstract

This research analyzes a seemingly malicious behavior known as a block withholding (BWH) attack between pools of cryptocurrency miners in Bitcoin-like systems featuring blockchain distributed databases. This work updates and builds on a seminal paper, The Miner's Dilemma, which studied a simplified scenario and showed that a BWH attack can be rational behavior that is profitable for the attacker. The new research presented here provides an in-depth profit analysis of a more complex and realistic BWH attack scenario, which includes mutual attacks between multiple, non-uniform Bitcoin mining pools. As a result of mathematical analysis and MATLAB modeling, this paper illustrates the Nash equilibrium conditions of a system of independent mining pools with varied mining rates and computes the equilibrium rates of mutual BWH attack. The analysis method quantifies the additional profit the largest pools extract from the system at the expense of the smaller pools. The results indicate that while the presence of BWH is a net negative for smaller pools, they must participate in BWH to maximize their remaining profits, and the results quantify the attack rates the smaller pools must maintain. Also, the smallest pools maximize profit by not attacking at all-that is, retaliation is not a rational move for them.