Incentives for stable mining in pay per last N shares pools

A large number of blockchain consensus protocols use the Proof of Work (PoW) principle, which relies on miners who exchange computation for newly minted currency. Their task is to support consensus, safeguarding the immutability of the chain’s history. For the sake of regular income, a vast majority of miners team-up in large independent pools. These pools distribute among all their members the rewards gathered from individual miners, thus guaranteeing a stable income for each miner in the pool. The monetary compensation follows a specific reward system enforced by the pool administrator. Pay Per Last N Shares (PPLNS) is one of the most popular reward systems in PoW pools. Despite many desirable properties, in this paper, we show that composition of PPLNS pools may be unstable. To better understand the incentives of miners, we explore the effect of time preferences in the mining decisions of miners. Using a game-theoretical model we study conditions for equilibrium in a game with two different PPLNS pools. We find that the range of parameters that support equilibria between the pools with large number of miners is minuscule. This implies that in many cases, miners may have incentives to migrate towards larger pools, harming decentralization in the process.