Towards a Theory of Maximal Extractable Value I: Constant Function Market Makers

Maximal Extractable Value (MEV) represents excess value captured by miners (or validators) from users in a cryptocurrency network. This excess value often comes from reordering users transactions to maximize fees or inserting new transactions that allow a miner to front-run users' transactions. The most common type of MEV involves what is known as a sandwich attack against a user trading on a popular class of automated market makers known as CFMMs. In this first paper of a series on MEV, we analyze game theoretic properties of MEV in CFMMs that we call \textit{reordering} and \textit{routing} MEV. In the case of reordering, we show conditions when the maximum price impact caused by the reordering of sandwich attacks in a sequence of trades relative to the average price impact is $O(\log n)$ in the number of user trades. In the case of routing, we present examples where the existence of MEV both degrades and counterintuitively \emph{improves} the quality of routing. We construct an analogue of the price of anarchy for this setting and demonstrate that if the impact of a sandwich attack is localized in a suitable sense, then the price of anarchy is constant. Combined, our results provide improvements that both MEV searchers and CFMM designers can utilize for estimating costs and profits of MEV.