An Economic Analysis of Difficulty Adjustment Algorithms in Proof‐of‐Work Blockchain Systems

ABSTRACT We study the stability of cryptocurrency systems through difficulty adjustment. Bitcoin's difficulty adjustment algorithm (DAA) exhibits instability when the reward elasticity of the hash rate is high, implying that a sharp price reduction could disrupt the current Bitcoin system. By contrast, newer DAAs developed and installed for other cryptocurrencies remain stably under substantially weaker conditions; thus, Bitcoin can inherently address this concern by upgrading its DAA. However, miners with high marginal costs profit from the existing DAA's instability and may oppose reforms that are beneficial for users. This finding highlights a critical challenge for the sustainability of cryptocurrencies.