Axioms for Constant Function Market Makers
研究了恒定乘积做市商（DeFi中常用）和对数市场评分规则做市商（预测市场中常用）的公理基础，用独立性和不变性公理刻画了这两类做市商，并证明了恒定乘积做市商在特定条件下的最优性。
ABSTRACT We study axiomatic foundations for different classes of automated market makers (AMMs). Our main results are a characterization of a generalization of constant product market makers (CPMMs), popular in decentralized finance, and a characterization of the Logarithmic Market Scoring Rule AMM, popular in prediction markets. The first class is characterized by the combination of independence and scale invariance, whereas the second is characterized by the combination of independence and translation invariance. The two classes are, therefore, distinguished by a different invariance property that is motivated by different interpretations of the numéraire in the two applications, but pinned down by the same separability property. Moreover, we characterize the CPMM as trader‐optimal among scale invariant, independent, symmetric and sufficiently funded AMMs. Our results add to a formal analysis of mechanisms used in practice and connect the most popular class of decentralized finance (DeFi) AMMs to the most popular class of prediction market AMMs.