Miners' Reward Elasticity and Stability of Competing Proof-of-Work Cryptocurrencies

Proof-of-Work cryptocurrencies employ miners to sustain the system through algorithmic reward adjustments. We develop a stochastic model of the multicurrency mining market and identify conditions for stable transaction speeds. Bitcoin's algorithm requires hash supply elasticity < 1 for stability, while ASERT remains stable for any elasticity and can be interpreted as a form of stochastic gradient descent under a certain loss function. Interactions with other currencies can relax Bitcoin's stability requirements. Using a halving event, we estimate miners' hash supply elasticity and conduct counterfactual simulations. Our findings reveal Bitcoin's heavy reliance on low hash supply elasticity and interactions with smaller cryptocurrencies, suggesting an algorithm upgrade is crucial for stability.