  We consider the impact of trading fees on the profits of arbitrageurs trading
against an automated marker marker (AMM) or, equivalently, on the adverse
selection incurred by liquidity providers due to arbitrage. We extend the model
of Milionis et al. [2022] for a general class of two asset AMMs to both
introduce fees and discrete Poisson block generation times. In our setting, we
are able to compute the expected instantaneous rate of arbitrage profit in
closed form. When the fees are low, in the fast block asymptotic regime, the
impact of fees takes a particularly simple form: fees simply scale down
arbitrage profits by the fraction of time that an arriving arbitrageur finds a
profitable trade.
