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Analysis of the Order Flow Auction under Proposer-Builder Separation

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  • Ruofei Ma
  • Wenpin Tang
  • David Yao

Abstract

In this paper, we consider the impact of the order flow auction (OFA) in the context of the proposer-builder separation (PBS) mechanism through a game-theoretic perspective. The OFA is designed to improve user welfare by redistributing maximal extractable value (MEV) to the users, in which two auctions take place: the order flow auction and the block-building auction. We formulate the OFA as a multiplayer game, and focus our analyses on the case of two competing players (builders). We prove the existence and uniqueness of a Nash equilibrium for the two-player game, and derive a closed-form solution by solving a quartic equation. Our result shows that the builder with a competitive advantage pays a relatively lower cost, leading to centralization in the builder space. In contrast, the proposer's shares evolve as a martingale process, which implies decentralization in the proposer (or, validator) space. Our analyses rely on various tools from stochastic processes, convex optimization, and polynomial equations. We also conduct numerical studies to corroborate our findings, and explore other features of the OFA under the PBS mechanism.

Suggested Citation

  • Ruofei Ma & Wenpin Tang & David Yao, 2025. "Analysis of the Order Flow Auction under Proposer-Builder Separation," Papers 2502.12026, arXiv.org.
    • Handle: RePEc:arx:papers:2502.12026
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    References listed on IDEAS

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    1. Tivas Gupta & Mallesh M Pai & Max Resnick, 2023. "The Centralizing Effects of Private Order Flow on Proposer-Builder Separation," Papers 2305.19150, arXiv.org, revised Oct 2023.
    2. Ioanid Roşu & Fahad Saleh, 2021. "Evolution of Shares in a Proof-of-Stake Cryptocurrency," Management Science, INFORMS, vol. 67(2), pages 661-672, February.
    3. Maryam Bahrani & Pranav Garimidi & Tim Roughgarden, 2024. "Centralization in Block Building and Proposer-Builder Separation," Papers 2401.12120, arXiv.org.
    4. Mallesh Pai & Max Resnick, 2023. "Structural Advantages for Integrated Builders in MEV-Boost," Papers 2311.09083, arXiv.org.
    5. Wenpin Tang & David D. Yao, 2022. "Polynomial Voting Rules," Papers 2206.10105, arXiv.org, revised Jan 2024.
    6. Wenpin Tang, 2022. "Stability of shares in the Proof of Stake Protocol -- Concentration and Phase Transitions," Papers 2206.02227, arXiv.org.
    7. Jiani Wu & Nguyen Khoi Tran, 2018. "Application of Blockchain Technology in Sustainable Energy Systems: An Overview," Sustainability, MDPI, vol. 10(9), pages 1-22, August.
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