Centralization in Block Building and Proposer-Builder Separation (2401.12120v1)

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

• The paper quantifies how heterogeneous block production rewards lead to centralization using rigorous game-theoretic and auction-based models.
• It reveals that even minor differences in block producer capabilities can trigger significant stake concentration through reinforcement dynamics.
• It demonstrates that an effective proposer-builder separation, supported by a competitive builder ecosystem, can mitigate centralization pressures.

Centralization in Block Building and Proposer-Builder Separation: A Game-Theoretic Analysis

The paper "Centralization in Block Building and Proposer-Builder Separation" by Bahrani, Garimidi, and Roughgarden explores the intricate dynamics of centralization within blockchain protocols, specifically focusing on block building and the concept of proposer-builder separation (PBS). The authors employ mathematical and game-theoretic models to challenge traditional assumptions and provide insights into the balance between decentralization and the specialized roles in block production.

Key Questions and Methodological Approach

The paper revolves around two pivotal questions:

1. Does the heterogeneity in skills and knowledge among block producers lead to centralization? If so, what are the economic forces and dynamics driving this?
2. How effective is the proposer-builder separation in maintaining decentralization among proposers? What role does the competitiveness of the builder ecosystem play?

To address these questions, the authors construct models connecting the dynamics of block production with economic theories such as Tullock contests, urn processes, and auction theory.

Main Findings

1. Economic and Game-Theoretic Models:
   • The analysis showcases that heterogeneous rewards among block producers can lead to a concentration of staking distribution.
   • Through a game-theoretic lens, the authors quantify how reward discrepancies contribute to centralization, with the equilibrium staking distribution influenced by differences in block producer capabilities.
2. Stochastic Processes and Reinforcement Dynamics:
   • The paper uses a stochastic model to illustrate how repeated reinvestment of rewards by sophisticated block producers accelerates stake concentration.
   • A significant finding indicates that even modest differences in reward capability can lead to substantial centralization over time.
3. Impact of Proposer-Builder Separation (PBS):
   • The separation of roles between proposers and builders is analyzed for its potential to reduce reward heterogeneity.
   • Under ideal conditions, where proposers engage only in validation and builders maximize block value independently, decentralization among proposers can be sustained.
   • The degree of separation's effectiveness highly depends on the competitiveness of the builder ecosystem, emphasizing the need for a diverse and capable set of builders.

Theoretical and Practical Implications

The authors' analysis has several critical implications:

• Theoretical Insights:
  • The models highlight the non-linear effects of heterogeneity on centralization, suggesting that system designers should prioritize mechanisms that minimize reward disparities.
  • Economic models inspired by Tullock contests provide a framework for understanding staking equilibria in heterogeneous environments.
• Practical Considerations:
  • The results advocate for robust PBS mechanisms to counteract centralization pressures by ensuring that builders contribute to block creation opportunities regardless of proposer identity.
  • The findings also suggest strategic interventions in reward structures to mitigate oligopoly formation within staking environments.

Speculations on Future Developments

The ongoing developments in blockchain technologies, particularly with the rise of decentralized finance (DeFi) and its integration with PBS, will likely continue to influence block production dynamics. Future research might explore further the intersection of economic incentives, technology-driven heterogeneities, and the socio-political dimensions of decentralization efforts.

In conclusion, this paper provides a rigorous analytical foundation to evaluate the forces driving centralization in blockchain protocols, advocating for methodologies and systems that can maintain the intended decentralization. The interplay of proposers and builders, if managed well, can support a more decentralized and equitable blockchain ecosystem.