In decentralized finance ("DeFi"), automated market makers (AMMs) enable traders to programmatically exchange one asset for another. Such trades are enabled by the assets deposited by liquidity providers (LPs). The goal of this paper is to characterize and interpret the optimal (i.e., profit-maximizing) strategy of a monopolist liquidity provider, as a function of that LP's beliefs about asset prices and trader behavior. We introduce a general framework for reasoning about AMMs. In this model, the market maker (i.e., LP) chooses a demand curve that specifies the quantity of a risky asset (such as BTC or ETH) to be held at each dollar price. Traders arrive sequentially and submit a price bid that can be interpreted as their estimate of the risky asset price; the AMM responds to this submitted bid with an allocation of the risky asset to the trader, a payment that the trader must pay, and a revised internal estimate for the true asset price. We define an incentive-compatible (IC) AMM as one in which a trader's optimal strategy is to submit its true estimate of the asset price, and characterize the IC AMMs as those with downward-sloping demand curves and payments defined by a formula familiar from Myerson's optimal auction theory. We characterize the profit-maximizing IC AMM via a generalization of Myerson's virtual values. The optimal demand curve generally has a jump that can be interpreted as a "bid-ask spread," which we show is caused by a combination of adverse selection risk (dominant when the degree of information asymmetry is large) and monopoly pricing (dominant when asymmetry is small).

翻译：在去中心化金融（DeFi）中，自动做市商（AMM）使交易者能够以编程方式将一种资产兑换为另一种资产。此类交易依赖于流动性提供者（LP）存入的资产。本文旨在描述并解释垄断流动性提供者的最优（即利润最大化）策略，该策略取决于LP对资产价格和交易者行为的信念。我们引入了一个通用框架来推理AMM。在该模型中，做市商（即LP）选择一条需求曲线，该曲线规定了在每个美元价格下应持有的风险资产（如BTC或ETH）数量。交易者顺序到达并提交一个价格出价，该出价可被解释为他们对风险资产价格的估计；AMM根据提交的出价，向交易者分配风险资产、要求交易者支付费用，并更新其对真实资产价格的内部估计。我们将激励相容（IC）的AMM定义为：交易者的最优策略是提交其对资产价格的真实估计，并证明IC的AMM具有向下倾斜的需求曲线，且其支付由梅尔森最优拍卖理论中的公式决定。通过推广梅尔森虚拟价值，我们刻画了利润最大化的IC AMM。最优需求曲线通常存在一个跳跃，可被解释为“买卖价差”，我们证明该价差源于逆向选择风险（在信息不对称程度较大时占主导）与垄断定价（在不对称程度较小时占主导）的共同作用。