Time-Dependent Decision-Making and Decentralization in Proof-of-Work Cryptocurrencies

Pool mining is a common way to reduce income variance for miners in Proof of Work Cryptocurrencies. A vast majority of mining does happen in pools, where a popular scheme to distribute rewards is Pay per last N Shares (PPLNS). In PPLNS and related schemes, miners are frequently making decisions whose rewards are not immediate and will only manifest in the future. This implies that models of inter-temporal utility are relevant when considering the incentives of miners. We show that when including these features of human behaviour in models of rational pool miners, the conditions that lead to decentralisation are hampered because larger pools may be more attractive to miners. We present a new game theoretical model of PPLNS where rational miners have time preferences. In this setup, the incentives of miners to work for a pool depend on the initial distribution of power between mining pools, as well as the specific details of how time is discounted. Agents jumping to larger pools face a trade-off between reducing the expected payoff from their shares in their current pool, or getting faster rewards in the future by joining a larger pool. We consider a case where pools of different mining power have the same size of reward window N. According to our study, in equilibrium larger pools have a tendency to accumulate a disproportionate share of the network power at the expense of smaller pools. This outcome is prevalent over a large range of realistic model parameters. Our model shows that PPLNS may be harmful to the decentralised governance of cryptocurrencies. A way to ameliorate these negative effects, is to encourage pools to have diverse window sizes, or use different reward mechanisms. Doing this in a decentralised fashion is an open challenge.