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Centralization in Block Building and Proposer-Builder Separation

Maryam Bahrani, Pranav Garimidi, Tim Roughgarden

TL;DR

The paper investigates centralization risks from block-producer heterogeneity and the potential of proposer-builder separation (PBS) to preserve decentralization. It develops a game-theoretic model with endogenous staking and heterogeneous rewards, a stochastic Pólya-urn framework for long-run staking, and an auction-theoretic PBS model with competitive builders; it proves a unique equilibrium and tight bounds on the top stake share, and analyzes the rate of concentration. It also shows that PBS can significantly reduce proposer heterogeneity when builders compete, with a quantifiable convergence as builder competition grows, though heavy-tailed builder values can undermine PBS in practice. Collectively, the results provide quantitative insights and design implications for maintaining decentralization in proof-of-stake blockchains through PBS and competitive block-building ecosystems.

Abstract

The goal of this paper is to rigorously interrogate conventional wisdom about centralization in block-building (due to, e.g., MEV and private order flow) and the outsourcing of block-building by validators to specialists (i.e., proposer-builder separation): 1. Does heterogeneity in skills and knowledge across block producers inevitably lead to centralization? 2. Does proposer-builder separation eliminate heterogeneity and preserve decentralization among proposers? This paper develops mathematical models and results that offer answers to these questions: 1. In a game-theoretic model with endogenous staking, heterogeneous block producer rewards, and staking costs, we quantify the extent to which heterogeneous rewards lead to concentration in the equilibrium staking distribution. 2. In a stochastic model in which heterogeneous block producers repeatedly reinvest rewards into staking, we quantify, as a function of the block producer heterogeneity, the rate at which stake concentrates on the most sophisticated block producers. 3. In a model with heterogeneous proposers and specialized builders, we quantify, as a function of the competitiveness of the builder ecosystem, the extent to which proposer-builder separation reduces the heterogeneity in rewards across different proposers. Our models and results take advantage of connections to contest design, Pólya urn processes, and auction theory.

Centralization in Block Building and Proposer-Builder Separation

TL;DR

The paper investigates centralization risks from block-producer heterogeneity and the potential of proposer-builder separation (PBS) to preserve decentralization. It develops a game-theoretic model with endogenous staking and heterogeneous rewards, a stochastic Pólya-urn framework for long-run staking, and an auction-theoretic PBS model with competitive builders; it proves a unique equilibrium and tight bounds on the top stake share, and analyzes the rate of concentration. It also shows that PBS can significantly reduce proposer heterogeneity when builders compete, with a quantifiable convergence as builder competition grows, though heavy-tailed builder values can undermine PBS in practice. Collectively, the results provide quantitative insights and design implications for maintaining decentralization in proof-of-stake blockchains through PBS and competitive block-building ecosystems.

Abstract

The goal of this paper is to rigorously interrogate conventional wisdom about centralization in block-building (due to, e.g., MEV and private order flow) and the outsourcing of block-building by validators to specialists (i.e., proposer-builder separation): 1. Does heterogeneity in skills and knowledge across block producers inevitably lead to centralization? 2. Does proposer-builder separation eliminate heterogeneity and preserve decentralization among proposers? This paper develops mathematical models and results that offer answers to these questions: 1. In a game-theoretic model with endogenous staking, heterogeneous block producer rewards, and staking costs, we quantify the extent to which heterogeneous rewards lead to concentration in the equilibrium staking distribution. 2. In a stochastic model in which heterogeneous block producers repeatedly reinvest rewards into staking, we quantify, as a function of the block producer heterogeneity, the rate at which stake concentrates on the most sophisticated block producers. 3. In a model with heterogeneous proposers and specialized builders, we quantify, as a function of the competitiveness of the builder ecosystem, the extent to which proposer-builder separation reduces the heterogeneity in rewards across different proposers. Our models and results take advantage of connections to contest design, Pólya urn processes, and auction theory.
Paper Structure (28 sections, 7 theorems, 28 equations, 1 figure)

This paper contains 28 sections, 7 theorems, 28 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Heterogeneity in rewards for block production.
  3. The centralizing forces of heterogeneity.
  4. Confining heterogeneity to block-building.
  5. Goal of this paper.
  6. Overview of Results
  7. Related Work
  8. Tullock contests.
  9. Proof of stake.
  10. Pólya urns.
  11. The Basic Model
  12. Discussion.
  13. Economic Forces Toward Centralization
  14. Competition Between Heterogeneous Block Producers
  15. Quantifying the Largest Market Share
  16. ...and 13 more sections

Key Result

Proposition 3.1

For every sequence $\mu_1 \ge \mu_2 \ge \cdots \ge \mu_n = 1$ of reward multipliers, every base reward $r$, and every cost parameter $c$, a vector $\hat{\mathbf{x}}$ is an equilibrium allocation if and only if it is a solution to the following optimization problem: subject to

Figures (1)

  • Figure 1: The maximum equilibrium market share of any BP with a BP set that is $(\gamma,k)$-competitive in the sense of Definition \ref{['d:gammak']}, as characterized by Theorem \ref{['t:BP_comp']}. The horizontal dotted line corresponds to a market share of 33%, which is a critical security threshold for many proof-of-stake blockchain protocols.

Theorems & Definitions (9)

  • Proposition 3.1: Characterizing Equilibria as Optima JT04
  • Definition 3.2: $(\gamma,k)$-competitive
  • Theorem 3.3: Characterization of the Maximum Market Share
  • Lemma 3.4: First Monotonicity Lemma
  • Definition 4.1: $\epsilon$-Centralization
  • Theorem 4.2: Bounds on Number of Blocks for $\epsilon$-Centralization
  • Theorem 5.1: Competition Reduces Proposer Heterogeneity
  • Lemma B.1: Second Monotonicity Lemma
  • Corollary B.2