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, P\'olya urn processes, and auction theory.

翻译：本文旨在严格审视关于区块构建中心化（例如由MEV和私有订单流导致）及验证者将区块构建外包给专业方（即提议者-构建者分离）的传统观点：1. 区块生产者之间技能和知识的异质性是否必然导致中心化？2. 提议者-构建者分离能否消除异质性并维护提议者间的去中心化？本文通过建立数学模型与结论，为上述问题提供解答：1. 在内生质押、异质性区块生产者奖励及质押成本的博弈论模型中，我们量化了异质性奖励对均衡质押分布集中程度的影响；2. 在异质性区块生产者持续将奖励再投资于质押的随机模型中，我们以生产者异质性为变量，量化了质押向最复杂生产者集中的速率；3. 在包含异质性提议者与专业化构建者的模型中，我们以构建者生态的竞争性为变量，量化了提议者-构建者分离在多大程度上降低了不同提议者间的奖励异质性。我们的模型与结论利用了对竞赛设计、波利亚瓮过程及拍卖理论的关联。