Reward Sharing Schemes for Stake Pools

TL;DR

This paper proposes reward sharing schemes for stake pools in proof-of-stake blockchains that incentivize fair formation, balance security and efficiency, and are resilient against various attacks, with demonstrated fast convergence in dynamic settings.

Contribution

It introduces parameterized reward sharing schemes that ensure desired pool numbers as Nash equilibria and analyzes their security, efficiency, and practical deployment in PoS systems.

Findings

Nash equilibria promote the desired number of pools.

Schemes balance inclusion of low-cost pools and protection against Sybil attacks.

Fast convergence to equilibria demonstrated in dynamic environments.

Abstract

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