Optimal Strategy in Longest-Chain Proof-of-Stake Mining with External Randomness

Abstract

The longest-chain Proof-of-Stake (PoS) mining protocol is an attractive energy-friendly alternative to the popular and successful Proof-of-Work (PoW) diagram. One foundational property of a blockchain protocol is its robustness against strategic manipulation, that all miners are incentivized to follow the honest mining strategy because no miner can defect from using the honest strategy and earn greater revenue. In this work, we closed the profit threshold gap by showing that it is a Nash equilibrium for all miners to play the honest mining strategy when no miner owns more than 32.34% of the stake. We presented Selfish Mining with Recovery (SMR), the optimal strategy for the PoS mining game with external randomness assuming a mining power of a^pos. We also proposed a computer-assisted algorithm that bounds the possible future profit for each state in the mining game, the result of which matches the optimal profit threshold implied by the optimal strategy.