Balancing Participation and Decentralization in Proof-of-Stake Cryptocurrencies

Proof-of-stake blockchain protocols have emerged as a compelling paradigm for organizing distributed ledger systems. In proof-of-stake (PoS), a subset of stakeholders participate in validating a growing ledger of transactions. For the safety and liveness of the underlying system, it is desirable for the set of validators to include multiple independent entities as well as represent a non-negligible percentage of the total stake issued. In this paper, we study a secondary form of participation in the transaction validation process, which takes the form of stake delegation, whereby an agent delegates their stake to an active validator who acts as a stake pool operator. We study reward sharing schemes that reward agents as a function of their collective actions regarding stake pool operation and delegation. Such payment schemes serve as a mechanism to incentivize participation in the validation process while maintaining decentralization. We observe natural trade-offs between these objectives and the total expenditure required to run the relevant reward schemes. Ultimately, we provide a family of reward schemes which can strike different balances between these competing objectives at equilibrium in a Bayesian game theoretic framework.