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

Automated Market Making and Arbitrage Profits in the Presence of Fees