The Specter (and Spectra) of Miner Extractable Value

TL;DR

This paper introduces a theoretical framework for quantifying the cost of miner extractable value (MEV), relating it to the smoothness of functions over permutations, and demonstrates its usefulness through examples and literature connections.

Contribution

It provides a simple, formal definition of the cost of MEV, explores its properties, and links it to mathematical concepts like function smoothness over the symmetric group.

Findings

The cost of MEV can be characterized mathematically.

The definition relates to the smoothness of functions over permutations.

The framework recovers existing results in the literature.

Abstract

Miner extractable value (MEV) refers to any excess value that a transaction validator can realize by manipulating the ordering of transactions. In this work, we introduce a simple theoretical definition of the 'cost of MEV', prove some basic properties, and show that the definition is useful via a number of examples. In a variety of settings, this definition is related to the 'smoothness' of a function over the symmetric group. From this definition and some basic observations, we recover a number of results from the literature.