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Tim Roughgarden
@tr
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
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Tim Roughgarden pfp
Tim Roughgarden
@tr
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
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Tim Roughgarden
@tr
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
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Tim Roughgarden
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Possible reasons for such heterogeneity across validators include: private orderflow of transactions, better block-building algorithms, profit from off-chain events, etc
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Tim Roughgarden pfp
Tim Roughgarden
@tr
Is conventional wisdom on centralization forces in block-building correct? We probe this question mathematically in two different models
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Tim Roughgarden pfp
Tim Roughgarden
@tr
In model #1, we consider a game-theoretic model with endogenous staking, heterogeneous block producer rewards, and staking costs
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Tim Roughgarden pfp
Tim Roughgarden
@tr
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
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Tim Roughgarden
@tr
In model #2, we study a stochastic process in which heterogeneous block producers repeatedly reinvest rewards into staking
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Tim Roughgarden pfp
Tim Roughgarden
@tr
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
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Tim Roughgarden pfp
Tim Roughgarden
@tr
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?
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Tim Roughgarden
@tr
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
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Tim Roughgarden pfp
Tim Roughgarden
@tr
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
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Tim Roughgarden
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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
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Tim Roughgarden
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Check out the full paper here: https://arxiv.org/pdf/2401.12120.pdf
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