  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.
