  In the ever evolving landscape of decentralized finance automated market
makers (AMMs) play a key role: they provide a market place for trading assets
in a decentralized manner. For so-called bluechip pairs, arbitrage activity
provides a major part of the revenue generation of AMMs but also a major source
of loss due to the so-called 'informed orderflow'. Finding ways to minimize
those losses while still keeping uninformed trading activity alive is a major
problem in the field. In this paper we will investigate the mechanics of said
arbitrage and try to understand how AMMs can maximize the revenue creation or
in other words minimize the losses. To that end, we model the dynamics of
arbitrage activity for a concrete implementation of a pool and study its
sensitivity to the choice of fee aiming to maximize the revenue for the AMM. We
identify dynamical fees that mimic the directionality of the price due to
asymmetric fee choices as a promising avenue to mitigate losses to toxic flow.
This work is based on and extends a recent article by some of the authors.
