Automated market makers (AMMs) are one of the most prominent decentralized finance (DeFi) applications. They allow users to exchange units of different types of crypto-assets, without the need to find a counter-party. There are several implementations and models for AMMs, featuring a variety of sophisticated economic mechanisms. We present a theory of AMMs. The core of our theory is an abstract operational model of the interactions between users and AMMs, which can be instantiated with any desired economic design mechanism. We exploit our theory to formally prove a set of fundamental properties of AMMs, characterizing both structural and economic aspects. We do this by abstracting from the actual economic mechanisms used in implementations, by identifying sufficient conditions which ensure the relevant properties. Notably, we devise a general solution to the arbitrage problem, the main game-theoretic foundation behind the economic mechanisms of AMMs.

中文翻译：

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DeFi中的自动做市商理论

自动做市商（AMM）是最著名的去中心化金融（DeFi）应用程序之一。它们允许用户交换不同类型的加密资产的单位，而无需寻找交易对手。AMM有多种实现和模型，具有多种复杂的经济机制。我们提出了AMM的理论。我们理论的核心是用户与AMM之间交互的抽象操作模型，可以使用任何所需的经济设计机制来实例化该模型。我们利用我们的理论来正式证明AMM的一系列基本特性，同时兼具结构和经济方面的特征。我们通过从实现中使用的实际经济机制中抽象出来，通过确定确保相关属性的充分条件来做到这一点。尤其，