Invariance properties of maximal extractable value

Paper: arXiv 2304.11010

Authors: Alan Guo

Abstract

We develop a formalism for reasoning about trading on decentralized exchanges on blockchains and a formulation of a particular form of maximal extractable value (MEV) that represents the total arbitrage opportunity extractable from on-chain liquidity. We use this formalism to prove that for blockchains with deterministic block times whose liquidity pools satisfy some natural properties that are satisfied by pools in practice, this form of MEV is invariant under changes to the ordering mechanism of the blockchain and distribution of block times. We do this by characterizing the MEV as the profit of a particularly simple arbitrage strategy when left uncontested. These results can inform design of blockchain protocols by ruling out designs aiming to increase trading opportunity by changing the ordering mechanism or shortening block times.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical formalism and formal proofs regarding MEV invariance across ordering mechanisms, scoring well on math complexity and novelty. However, it lacks empirical validation, backtesting on historical blockchain data, or statistical testing, putting it squarely in the theoretical category.

Research Flowchart

  flowchart TD
    A[Research Goal: Assess impact of block times & orderings on MEV] --> B[Formalize DEX Liquidity Pools & Arbitrage MEV]
    B --> C[Inputs: Deterministic block times & natural pool properties]
    C --> D[Characterize MEV as uncontested simple arbitrage strategy]
    D --> E[Prove Arbitrage Invariance Theorem]
    E --> F[Outcome: Protocol reordering or faster block times do not alter MEV]