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.

中文翻译：

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权益证明区块链的中心化：引导协议的博弈论分析

权益证明 (PoS) 已成为资源密集型工作量证明 (PoW) 区块链的自然替代品，正如最近的以太坊合并所体现的那样。基于 PoS 的区块链需要在参与者之间进行初始股权分配。通常，这种初始权益分配称为引导。本文认为现有的引导协议很容易集中化。为了解决引导导致的中心化问题，我们提出了一种新颖的游戏 $\Gamma_\textsf{bootstrap}$。接下来，我们定义三个条件：（i）个体理性（IR），（ii）激励相容性（IC），以及（iii）$(\tau,\delta,\epsilon)-$去中心化引导协议必须满足。 $(\tau,\delta,\epsilon)$ 是量化去中心化的某些参数。为此，我们提出了一种新的中心化指标 C-NORM 来衡量 PoS 系统中的中心化程度。我们定义一个中心化游戏——$\Gamma_\textsf{cent}$，来分析中心化指标的有效性。我们证明，在存在能够发起 Sybil 攻击的战略参与者的情况下，C-NORM 有效地捕获了中心化。通过 C-NORM，我们分析了流行的引导协议，例如 Airdrop 和 Proof-of-Burn (PoB)，并证明它们分别不满足 IC 和 IR。受以太坊合并的推动，我们研究了 W2SB（一种基于 PoW 的引导协议）并证明它是理想的。此外，我们还进行综合模拟，以实证验证 W2SB 自举 PoS 是去中心化的。