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 based on a Bayesian-like belief inference framework, where LPs maintain an asset price estimate. In this model, the market maker (i.e., LP) chooses a demand curve that specifies the quantity of a risky asset 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 generalize Myerson's virtual values, and characterize the profit-maximizing IC AMM. 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). This work opens up new research directions into the study of automated exchange mechanisms from the lens of optimal auction theory and iterative belief inference, using tools of theoretical computer science in a novel way.

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实现一种资产与另一种资产的交换。此类交易由流动性提供者（LP）存入的资产支撑。本文旨在刻画并解释垄断流动性提供者的最优（即利润最大化）策略，该策略依赖于LP对资产价格及交易者行为的信念。我们引入了一个基于类贝叶斯信念推理框架的通用体系，用以推理AMM，其中LP维持一个资产价格估计。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数量。交易者依次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根据该提交的出价，向交易者分配风险资产，要求交易者支付相应款项，并更新对真实资产价格的内部估计。我们将激励兼容（IC）的AMM定义为：交易者的最优策略是提交其真实资产价格估计的机制；并刻画IC AMM的特征为具有向下倾斜的需求曲线，且支付项由迈尔森最优拍卖理论中熟悉的公式定义。我们推广了迈尔森的虚拟估值，并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"，我们证明这是由逆向选择风险（在信息不对称程度较大时占主导）和垄断定价（在信息不对称较小时占主导）共同造成的。本工作开辟了通过最优拍卖理论和迭代信念推理视角研究自动交换机制的新方向，并以新颖的方式运用了理论计算机科学的工具。