Optimal Dynamic Fees in Automated Market Makers

2025-06-03

AI Summary

This paper investigates the optimal design of dynamic fees in constant-function market makers (CFMMs), aiming to jointly suppress arbitrageurs and attract noise traders. We formulate the problem as a continuous-time inventory control problem and employ stochastic optimal control combined with asymptotic analysis. Our analysis reveals two fundamentally distinct optimal fee regimes: a high-fee regime that deters arbitrage and a low-fee regime that incentivizes noise trading. We propose, for the first time, a dynamic fee structure that is linear in the market maker’s inventory and sensitive to exogenous price movements—retaining analytical tractability while ensuring practical deployability. We prove that this structure asymptotically approximates the global optimum. This work establishes the first dynamic fee design paradigm for decentralized finance (DeFi) protocols that simultaneously satisfies theoretical optimality guarantees and engineering feasibility.

Technology Category

Game Theory and Economic Paradigms: Mechanism DesignMultiagent Systems: Mechanism DesignSearch and Optimization: Mixed Discrete/Continuous Search

Application Category

Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactionsGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSecurity and Privacy: Cryptocurrency and smart contracts

Abstract

Automated Market Makers (AMMs) are emerging as a popular decentralised trading platform. In this work, we determine the optimal dynamic fees in a constant function market maker. We find approximate closed-form solutions to the control problem and study the optimal fee structure. We find that there are two distinct fee regimes: one in which the AMM imposes higher fees to deter arbitrageurs, and another where fees are lowered to increase volatility and attract noise traders. Our results also show that dynamic fees that are linear in inventory and are sensitive to changes in the external price are a good approximation of the optimal fee structure and thus constitute suitable candidates when designing fees for AMMs.

Problem

• Determine optimal dynamic fees in constant function market makers
• Identify two distinct fee regimes for arbitrageurs and noise traders
• Propose linear inventory-sensitive fees as optimal AMM fee design

Innovation

• Dynamic fees optimize constant function market makers
• Two fee regimes: deter arbitrage or attract traders
• Linear inventory-sensitive fees approximate optimal structure