Routing MEV in Constant Function Market Makers

Miner 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 decentralized exchange. We analyze game theoretic properties of MEV in CFMMs that we call routing MEV, where an aggregate user trade is routed over a network and potentially sandwich attacked. We present examples where the existence of routing 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 (The code for all the numerical experiments in this paper can be found at this link: https://github.com/tjdiamandis/mev-cfmm ).