Blockchains have popularized automated market makers (AMMs). An AMM exchange is an application running on a blockchain which maintains a pool of crypto-assets and automatically trades assets with users governed by some pricing function that prices the assets based on their relative demand/supply. AMMs have created an important challenge commonly known as the Miner Extractable Value (MEV). In particular, the miners who control the contents and ordering of transactions in a block can extract value by front-running and back-running users' transactions, leading to arbitrage opportunities that guarantee them risk-free returns. In this paper, we consider how to design AMM mechanisms that eliminate MEV opportunities. Specifically, we propose a new AMM mechanism that processes all transactions contained within a block in a batch. We show that our new mechanism satisfies two tiers of guarantees. First, for legacy blockchains where each block is proposed by a single (possibly rotating) miner, we prove that our mechanism satisfies arbitrage resilience, i.e., a miner cannot gain risk-free profit. Moreover, we also guarantee fair treatment among all transactions within the same block, such that the miner is unable to sell off favorable positions in the block to users or arbitragers. Second, for blockchains where the block proposal process is decentralized and offers sequencing-fairness, we prove a stronger notion called incentive compatibility -- roughly speaking, we guarantee that any individual user's best response is to follow the honest strategy.

翻译：区块链技术使自动做市商（AMM）得以普及。AMM交易所是运行在区块链上的应用程序，它维护一个加密资产池，并根据某种基于资产相对供需关系进行定价的定价函数，自动与用户进行资产交易。AMM引发了一个重要挑战，即通常所说的矿工可提取价值（MEV）。具体而言，控制区块内交易内容与排序的矿工，可以通过抢先交易（front-running）和尾随交易（back-running）用户交易来提取价值，从而产生确保其无风险收益的套利机会。本文探讨如何设计消除MEV机会的AMM机制。具体地，我们提出一种新的AMM机制，该机制将区块内的所有交易进行批处理。我们证明新机制满足两层保障：首先，对于每个区块由单个（可能轮换的）矿工提出的传统区块链，我们证明该机制具有抗套利性，即矿工无法获得无风险利润。此外，我们保证了同一区块内所有交易的公平处理，使得矿工无法向用户或套利者出售区块内的有利排序位置。其次，对于区块提议过程去中心化且提供排序公平性的区块链，我们证明了更强的概念——激励相容性——大致而言，我们保证任何单个用户的最佳响应是遵循诚实策略。