Towards a Theory of Maximal Extractable Value II: Uncertainty

Maximal Extractable Value (MEV) is value extractable by temporary monopoly power commonly found in decentralized systems. This extraction stems from a lack of user privacy upon transaction submission and the ability of a monopolist validator to reorder, add, and/or censor transactions. There are two main directions to reduce MEV: reduce the flexibility of the miner to reorder transactions by enforcing ordering rules and/or introduce a competitive market for the right to reorder, add, and/or censor transactions. In this work, we unify these approaches via \emph{uncertainty principles}, akin to those found in harmonic analysis and physics. This provides a quantitative trade-off between the freedom to reorder transactions and the complexity of an economic payoff to a user in a decentralized network. This trade off is analogous to the Nyquist-Shannon sampling theorem and demonstrates that sequencing rules in blockchains need to be application specific. Our results suggest that neither so-called fair ordering techniques nor economic mechanisms can individually mitigate MEV for arbitrary payoff functions.