A theoretical framework for fees in AMMs

TL;DR

This paper develops a theoretical framework to analyze and optimize fee structures in automated market makers (AMMs) to balance arbitrage revenue and loss minimization, enhancing understanding of AMM dynamics.

Contribution

It introduces a model of arbitrage activity in AMMs, linking fee choices to revenue and loss dynamics, and maps these to a random walk with rewards for further analysis.

Findings

Model of arbitrage dynamics in AMMs

Sensitivity analysis of fees on revenue and losses

Mapping to a random walk with rewards for future studies

Abstract

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 value retention. We manage to map the ensuing dynamics to that of a random walk with a specific reward scheme that provides a convenient starting point for further studies.