Centralization in Proof-of-Stake Blockchains: A Game-Theoretic Analysis of Bootstrapping Protocols

TL;DR

This paper analyzes the centralization risks in proof-of-stake blockchain bootstrapping protocols using game theory, proposing a new metric C-NORM and evaluating protocols like Airdrop, PoB, and W2SB for decentralization.

Contribution

It introduces a novel game-theoretic framework and a new centralization metric C-NORM to evaluate and improve bootstrapping protocols in PoS blockchains.

Findings

C-NORM effectively measures centralization with strategic players.

Airdrop and PoB protocols do not satisfy incentive compatibility and individual rationality.

W2SB protocol is shown to be ideal and empirically decentralized.

Abstract

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.