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 algorithm 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.