A Note on Optimal Fees for Constant Function Market Makers

TL;DR

This paper develops a theoretical framework to determine optimal trading fees for constant function market makers, ensuring stable equilibrium fees that maximize liquidity provider returns and influence capital allocation.

Contribution

It introduces a model for optimal fee setting in CFMMs, proves the existence of Nash equilibria, and applies the framework to real-world data for practical fee computation.

Findings

Existence of pure Nash equilibria for optimal fees

Optimal fees influence capital distribution among pools

Framework applicable to real-world CFMMs

Abstract

We suggest a framework to determine optimal trading fees for constant function market makers (CFMMs) in order to maximize liquidity provider returns. In a setting of multiple competing liquidity pools, we show that no race to the bottom occurs, but instead pure Nash equilibria of optimal fees exist. We theoretically prove the existence of these equilibria for pools using the constant product trade function used in popular CFMMs like Uniswap. We also numerically compute the equilibria for a number of examples and discuss the effects the equilibrium fees have on capital allocation among pools. Finally, we use our framework to compute optimal fees for real world pools using past trade data.