  Within this work we consider an axiomatic framework for Automated Market
Makers (AMMs). By imposing reasonable axioms on the underlying utility
function, we are able to characterize the properties of the swap size of the
assets and of the resulting pricing oracle. In providing these general AMM
axioms, we define a novel measure of price impacts that can be used to quantify
those costs between different constructions. We have analyzed many existing
AMMs and shown that the vast majority of them satisfy our axioms. We have also
considered the question of fees and divergence loss. In doing so, we have
proposed a new fee structure so as to make the AMM indifferent to transaction
splitting. Finally, we have proposed a novel AMM that has nice analytical
properties and provides a large range over which there is no divergence loss.
