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

Maximal Extractable Value (MEV) refers to 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 from inserting new transactions that front-run users' transactions. One of the most common types of MEV involves a `sandwich attack' against a user trading on a constant function market maker (CFMM), which is a popular class of automated market maker. We analyze game theoretic properties of MEV in CFMMs that we call textitrouting and textitreordering MEV. In the case of routing, we present examples where the existence of MEV both degrades and, counterintuitively, 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. 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. Combined, our results suggest methods that both MEV searchers and CFMM designers can utilize for estimating costs and profits of MEV.