Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Varul Srivastava, Sankarshan Damle, Sujit Gujar

TL;DR

This paper addresses the centralization risk that arises during bootstrapping in Proof-of-Stake blockchains by modeling bootstrapping as a game, Γ_bootstrap, with a clear set of objectives: Individual Rationality (IR), Incentive Compatibility (IC), and $(\tau,\delta,\epsilon)$-Decentralization. It introduces C-NORM, a robust centralization metric derived from a PoS System Graph that accounts for dynamic participant arrival and Sybil attacks, and formalizes a centralization game Γ_cent to test the discriminative power of centralization metrics. The authors show that popular bootstrapping schemes like Airdrop and Proof-of-Burn fail IC and IR respectively, while a PoW-based bootstrapping protocol W2SB satisfies IR, IC, and decentralization, and can achieve any desired decentralization level in finite rounds (with empirical validation). The work provides a rigorous framework for evaluating bootstrapping protocols and demonstrates, via theory and simulations, that careful bootstrapping design can drive PoS systems toward decentralization with practical implications for secure and fair blockchain governance.

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 $Γ_\textsf{bootstrap}$. Next, we define three conditions: (i) Individual Rationality (IR), (ii) Incentive Compatibility (IC), and (iii) $(τ,δ,ε)-$ Decentralization that an \emph{ideal} bootstrapping protocol must satisfy. $(τ,δ,ε)$ 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 -- $Γ_\textsf{cent}$, 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.

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

TL;DR

This paper addresses the centralization risk that arises during bootstrapping in Proof-of-Stake blockchains by modeling bootstrapping as a game, Γ_bootstrap, with a clear set of objectives: Individual Rationality (IR), Incentive Compatibility (IC), and -Decentralization. It introduces C-NORM, a robust centralization metric derived from a PoS System Graph that accounts for dynamic participant arrival and Sybil attacks, and formalizes a centralization game Γ_cent to test the discriminative power of centralization metrics. The authors show that popular bootstrapping schemes like Airdrop and Proof-of-Burn fail IC and IR respectively, while a PoW-based bootstrapping protocol W2SB satisfies IR, IC, and decentralization, and can achieve any desired decentralization level in finite rounds (with empirical validation). The work provides a rigorous framework for evaluating bootstrapping protocols and demonstrates, via theory and simulations, that careful bootstrapping design can drive PoS systems toward decentralization with practical implications for secure and fair blockchain governance.

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 . Next, we define three conditions: (i) Individual Rationality (IR), (ii) Incentive Compatibility (IC), and (iii) Decentralization that an \emph{ideal} bootstrapping protocol must satisfy. 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 -- , 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.
Paper Structure (59 sections, 6 theorems, 10 equations, 4 figures, 2 tables, 1 algorithm)

This paper contains 59 sections, 6 theorems, 10 equations, 4 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. The Bootstrapping Model.
  3. Quantifying Centralization.
  4. C-NORM.
  5. The Centralization Game $(\Gamma_\textsf{cent})$.
  6. Our Contributions.
  7. Related Work
  8. Bootstrapping in Blockchains.
  9. Centralization in Networks and Multi-Agent Systems.
  10. Preliminaries
  11. Blockchain Preliminaries
  12. Proof-of-Work (PoW) Nakamoto2009.
  13. Proof-of-Stake (PoS) posOuroboros2018.
  14. Proof-of-Burn (PoB) PoB2020.
  15. Airdrop AirdropSybil.
  16. ...and 44 more sections

Key Result

Theorem 1

In $\Gamma_{cent}\langle\{M_{C},M_{D}\},S_{SA},e_{r},\Omega^{\star},\kappa\rangle$, for any $(s_{0},s_{1})$ chosen by $M_{C}$ from the set $\{(s_{0},s_{1})\;:\;s_{0} \in S_{SA} , s_{1} = e_{r}(s_{0})\}$, if $M_{D}$ uses metric C-NORM ($\Omega^{\star}$) then $Pr(D_{\kappa}(\Omega^{\star}) = 1) > 1 -

Figures (4)

  • Figure 1: The Centralization Game
  • Figure 2: C-NORM against rounds for different stopping time $T$ for distribution $\mathcal{N}(7,3)$
  • Figure 3: C-NORM against rounds for different $T$ and different distributions of miner stake
  • Figure 4: PoS System graph and cycle elimination.

Theorems & Definitions (14)

  • definition 1: Individual Rationality (IR)
  • definition 2: Nash Incentive Compatibility (IC)
  • definition 3: $(\tau,\delta,\epsilon)-$Decentralization
  • definition 4: Ideal Bootstrapping Protocol
  • definition 5: C-Norm $(\Omega)$
  • Example 1: Analysing centralization metrics using $\Gamma_{cent}$
  • Theorem 1
  • Theorem 2
  • Claim 1
  • Claim 2
  • ...and 4 more