Proof-of-stake (PoS) has emerged as a natural alternative to the resource-intensive Proof-of-Work (PoW) blockchain, as was recently seen with the Ethereum Merge. PoS-based blockchains require an initial stake distribution among the participants. Typically, this initial stake distribution is called bootstrapping. This paper argues that existing bootstrapping protocols are prone to centralization. To address centralization due to bootstrapping, we propose a novel game $\Gamma_\textsf{bootstrap}$. Next, we define three conditions: (i) Individual Rationality (IR), (ii) Incentive Compatibility (IC), and (iii) $(\tau,\delta,\epsilon)-$ Decentralization that an \emph{ideal} bootstrapping protocol must satisfy. $(\tau,\delta,\epsilon)$ are certain parameters to quantify decentralization. Towards this, we propose a novel centralization metric, C-NORM, to measure centralization in a PoS System. We define a centralization game -- $\Gamma_\textsf{cent}$, to analyze the efficacy of centralization metrics. We show that C-NORM effectively captures centralization in the presence of strategic players capable of launching Sybil attacks. With C-NORM, we analyze popular bootstrapping protocols such as Airdrop and Proof-of-Burn (PoB) and prove that they do not satisfy IC and IR, respectively. Motivated by the Ethereum Merge, we study W2SB (a PoW-based bootstrapping protocol) and prove it is ideal. In addition, we conduct synthetic simulations to empirically validate that W2SB bootstrapped PoS is decentralized.

翻译：权益证明（PoS）已成为资源密集型工作量证明（PoW）区块链的自然替代方案，近期以太坊合并便是例证。基于PoS的区块链需要在参与者间进行初始权益分配，这一过程通常称为引导。本文论证现有引导协议存在中心化倾向。针对引导导致的中心化问题，我们提出新型博弈$\Gamma_\textsf{bootstrap}$。继而定义理想引导协议需满足的三个条件：（i）个体理性（IR）、（ii）激励相容性（IC）以及（iii）$(\tau,\delta,\epsilon)-$去中心化，其中$(\tau,\delta,\epsilon)$为量化去中心化程度的特定参数。为此，我们提出新型中心化度量指标C-NORM以衡量PoS系统的中心化程度。通过定义中心化博弈$\Gamma_\textsf{cent}$来分析中心化度量指标的有效性，证明C-NORM能有效捕捉存在可发起女巫攻击的策略型玩家时的中心化现象。利用C-NORM，我们分析了空投和燃烧证明（PoB）等主流引导协议，证明其分别不满足IC与IR条件。受以太坊合并启发，我们研究基于PoW的引导协议W2SB，证明其具有理想特性。此外，通过合成仿真实验实证验证基于W2SB引导的PoS系统具有去中心化特征。