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We introduce and study reward sharing schemes (RSS) that promote the fairformation of {\em stake pools}\ in collaborative projects that involve a largenumber of stakeholders such as the maintenance of a proof-of-stake (PoS)blockchain. Our mechanisms are parameterized by a target value for the desirednumber of pools. We show that by properly incentivizing participants, thedesired number of stake pools is a Nash equilibrium arising from rational play.Our equilibria also exhibit an efficiency / security tradeoff via a parameterthat calibrates between including pools with the smallest cost and providingprotection against Sybil attacks, the setting where a single stakeholdercreates a large number of pools in the hopes to dominate the collaborativeproject. We then describe how RSS can be deployed in the PoS setting,mitigating a number of potential deployment attacks and protocol deviationsthat include censoring transactions, performing Sybil attacks with theobjective to control the majority of stake, lying about the actual cost andothers. Finally, we experimentally demonstrate fast convergence to equilibriain dynamic environments where players react to each other's strategic movesover an indefinite period of interactive play. We also show how simple rewardsharing schemes that are seemingly more "fair", perhaps counterintuitively,converge to centralized equilibria.

Reward Sharing Schemes for Stake Pools