Analysis of the Order Flow Auction under Proposer-Builder Separation on Blockchain

Abstract

We study the impact of the order flow auction (OFA) in the context of the proposer-builder separation (PBS) mechanism in blockchains 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 sequential auctions take place: the order flow auction and the block-building auction. We formulate the OFA as a multiplayer game, and establish the existence of a Nash equilibrium, and in the two-player case derive a closed-form solution (and prove its uniqueness) via a quartic equation. Our result shows that the builder with a competitive advantage pays a lower cost, leading to a higher revenue, and adding to centralization in the builder space. In contrast, the proposer's shares evolve as a martingale process, which implies decentralization in the proposer/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 to bring out other features of the OFA under the PBS mechanism.