  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 payment 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 payment schemes. Ultimately,
we provide a family of payment schemes which can strike different balances
between these competing objectives at equilibrium in a Bayesian game theoretic
framework.
