Axioms for Constant Function Market Makers

We study axiomatic foundations for different classes of constant function automated market makers (CFMMs). We focus particularly on separability and homogeneity properties and give axiomatic characterizations of a natural generalization of constant product market makers (CPMMs). Moreover, we characterize the CPMM as an extremal point within the class of homogenuous, independent, symmetric AMMs with non-concentrated liquidity provision. Our results add to a formal analysis of mechanisms that are currently used for decentralized exchanges and introduce new tools to the topic.