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 \textit{routing} and \textit{reordering} MEV. 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. 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.

翻译：最大化可提取价值（MEV）指加密货币网络中矿工（或验证者）从用户处捕获的超额价值。这种超额价值通常源于对用户交易进行重排序以最大化手续费收入，或插入抢先于用户交易的新交易。最常见的MEV类型之一是对在常数函数做市商（CFMM，一类流行的自动做市商）上交易的用户实施"夹击攻击"。我们分析了CFMM中称为*路由*与*重排序*MEV的博弈论特性。在路由情形下，我们给出示例表明MEV的存在既可能降低路由质量，也可能（反直觉地）*改善*路由质量。我们为这一场景构建了无政府价格（price of anarchy）的类比物，并证明若夹击攻击的影响在适当意义上局部化，则该无政府价格为常数。在重排序情形下，我们证明了当连续交易序列中由夹击攻击重排序引发的最大价格冲击相对于平均价格时，该冲击为$O(\log n)$（其中$n$为用户交易数量）。综合而言，我们的研究结果提出了MEV搜寻者与CFMM设计者均可用于估算MEV成本与收益的方法。