最优自动做市商：可微经济学与强对偶性
Optimal Automated Market Makers: Differentiable Economics and Strong Duality
AI总结：
本文研究多商品及逆向选择下的最优自动做市商设计，证明其与最优传输问题对偶，并利用可微经济学工具发现最优机制可通过捆绑策略和实物支付提升效率。
摘要：
做市商的角色是同时提出以指定价格买卖一定数量的商品，通常是金融资产（如股票）。自动做市商（AMM）是一种根据预定计划进行交易的机制；该计划的最佳选择取决于做市商的目标。关于AMM设计的文献主要集中在以信息 elicitation 为目标的预测市场上。受 DeFi 启发的较新工作则转向以利润最大化为目标，但仅考虑单一类型的商品（与一种计价单位进行交易），包括在逆向选择下（Milionis et al. 2022）。在存在多种商品的情况下，包括可能出现的复杂捆绑行为，最优做市机制尚不明确。在本文中，我们证明了寻找最优做市商与最优传输问题对偶，且对偶中的传输计划具有特定的几何约束。我们表明，针对多种商品且在逆向选择下的最优机制可以利用捆绑策略，既能改善捆绑买卖的价格，有时还能接受“实物”支付。我们提出了在额外设定下最优机制的猜想，这些猜想展示了更复杂的行为。从方法论角度看，我们实质性地利用了可微经济学工具来生成最优机制的猜想，并为使用此类工具指导理论研究提供了概念验证。
英文摘要：
The role of a market maker is to simultaneously offer to buy and sell quantities of goods, often a financial asset such as a share, at specified prices. An automated market maker (AMM) is a mechanism that offers to trade according to some predetermined schedule; the best choice of this schedule depends on the market maker's goals. The literature on the design of AMMs has mainly focused on prediction markets with the goal of information elicitation. More recent work motivated by DeFi has focused instead on the goal of profit maximization, but considering only a single type of good (traded with a numeraire), including under adverse selection (Milionis et al. 2022). Optimal market making in the presence of multiple goods, including the possibility of complex bundling behavior, is not well understood. In this paper, we show that finding an optimal market maker is dual to an optimal transport problem, with specific geometric constraints on the transport plan in the dual. We show that optimal mechanisms for multiple goods and under adverse selection can take advantage of bundling, both improved prices for bundled purchases and sales as well as sometimes accepting payment "in kind." We present conjectures of optimal mechanisms in additional settings which show further complex behavior. From a methodological perspective, we make essential use of the tools of differentiable economics to generate conjectures of optimal mechanisms, and give a proof-of-concept for the use of such tools in guiding theoretical investigations.
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