In a Proof-of-Work blockchain the equilibrium hashrate is a monotone function of the fiat exchange value of the block reward. There is no lower or upper bound on hashrate. This creates two types of inefficiency. First, the vulnerability to an attack increases as hashrate falls since (we argue) the profitability of a double-spend or disruptive attack is a function of the hashrate required to gain control of the network. Second, external costs grow as hashrate rises. Hashing consumes electricity which contributes to global warming and increases the cost of energy for alternative uses. There is an interval of hashrate within which the combined costs are minimized.
We propose a modification of the Proof-of-Work protocol that, for a target interval, incentivizes miners to push hashrate toward the interval. When hashrate drops below the lower bound, the miner receives a supplemental reward which induces increased hashrate. When hashrate exceeds the upper bound, the miner receives a fraction of the block reward, which induces reduced hashrate. Puzzle difficulty, a sufficient statistic for hashrate, governs the adjustment to the miner’s reward. Monetary neutrality can be maintained by balancing the reduced reward when hashrate is above target with the supplement to the reward when hashrate is below target.