  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.
