  This paper studies the question whether automated market maker protocols such
as Uniswap can sustainably retain a portion of their trading fees for the
protocol. We approach the problem by modelling how to optimally choose a pool's
take rate, i.e\ the fraction of fee revenue that remains with the protocol, in
order to maximize the protocol's revenue. The model suggest that if AMMs have a
portion of loyal trade volume, they can sustainably set a non-zero take rate,
even without losing liquidity to competitors with a zero take rate.
Furthermore, we determine the optimal take rate depending on a number of model
parameters including how much loyal trade volume pools have and how high the
competitors' take rates are.
