A theoretical framework for fees in AMMs

2024-04-05

AI Summary

In decentralized finance (DeFi), arbitrage against blue-chip asset pairs in automated market makers (AMMs) constitutes a primary revenue source but also induces substantial impermanent loss (IL) due to informed order flow. The central challenge lies in suppressing informed arbitrage while preserving liquidity for uninformed trades. Method: This paper introduces the first analytical model of AMM arbitrage dynamics as a stochastic walk with state-dependent rewards, yielding a tractable theoretical framework for fee optimization. Through rigorous stochastic process analysis, sensitivity analysis, and quantification of value retention, we derive closed-form relationships between fee rates and pool asset value preservation. Results: We formally prove the existence of an optimal fee rate and characterize its structural properties—balancing revenue generation against IL mitigation. This work establishes the first analytically rigorous and practically actionable paradigm for designing AMM fee mechanisms.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Other Foundations of Search & Optimization

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Minimizing AMM losses from informed arbitrage activity
• Optimizing fee structures to maximize revenue retention
• Modeling arbitrage dynamics as a reward-based random walk

Innovation

• Modeling arbitrage dynamics in AMM pools
• Mapping dynamics to reward-based random walk
• Optimizing fee sensitivity for value retention