Proposer-builder separation (PBS) plays a major role in Ethereum's current block-building process. But is PBS a good design? Is it really necessary? A new paper with Maryam Bahrani and @pgarimidi develops the theory necessary for reasoning rigorously about these questions

Head of research at a16z crypto.
Professor, Columbia University.

Background: The idea of PBS is to split out the role of assembling a block of transactions from the other duties of the validator, with the goal of preserving decentralization in the validator set despite potential centralizing forces in block-building

We begin with Ethereum circa 2020, in which each validator builds its own blocks. We're interested in the case in which some validators can extract more revenue from a block production opportunities than others

Possible reasons for such heterogeneity across validators include: private orderflow of transactions, better block-building algorithms, profit from off-chain events, etc

Is conventional wisdom on centralization forces in block-building correct? We probe this question mathematically in two different models

In model #1, we consider a game-theoretic model with endogenous staking, heterogeneous block producer rewards, and staking costs

Building on connections to Tullock contests, the main result here quantifies the concentration in the equilibrium staking distribution as a function of how many other validators k are within a fraction γ of their rewards

In model #2, we study a stochastic process in which heterogeneous block producers repeatedly reinvest rewards into staking

Building on connections to Pólya urns and Yule processes, the main result here quantifies, as a function of the block producer heterogeneity, how many blocks it takes before stake concentrates on the most sophisticated block producers

Thus economic and probabilistic arguments both show that leveling the playing field across validators can go a long way toward a more decentralized allocation of stake. But fast forwarding to present-day Ethereum, does PBS achieve such a leveling?

In our idealized model of PBS, k builders with i.i.d. block valuations compete in a first price auction. The proposer of a slot can also attempt to build its own block, with value drawn from a distribution dominated by the builder distribution

Our main result in this model of PBS is a positive one: under a common distributional assumption ("monotone hazard rate"), PBS ensures that no validator earns much more than another from a given block production opportunity

Tl;dr: our results formalize the forces toward centralization in block-building and the pushback provided by PBS. We hope that other researchers develop their own models and results to help the community better understand PBS and its pros and cons versus alternative designs

Check out the full paper here: https://arxiv.org/pdf/2401.12120.pdf