Axioms for Constant Function AMMs

We study axiomatic foundations for different classes of constant function automated market makers (AMMs). We focus particularly on independence, homogeneity and convexity properties and give axiomatic characterizations of a natural generalization of constant product AMMs that has not been considered so far in the decentralized finance context. Our results add to a formal analysis of mechanisms that are currently used for decentralized exchanges and introduces tools of decision theory to the topic.