Competition between DEXs through Dynamic Fees

TL;DR

This paper models the strategic fee-setting behavior of competing decentralized exchanges (DEXs), revealing how competition influences fee dynamics, market stability, and trader outcomes through a game-theoretic and PDE-based analysis.

Contribution

It introduces a coupled PDE model to characterize equilibrium fees among competing DEXs and derives approximate closed-form solutions, extending monopoly models to competitive settings.

Findings

Competition reduces execution slippage for liquidity takers.

Increased number of DEXs lowers fee revenue per DEX.

Market activity level determines noise traders' slippage impact.

Abstract

We find an approximate Nash equilibrium in a game between decentralized exchanges (DEXs) that compete for order flow by setting dynamic trading fees. We characterize the equilibrium via a coupled system of partial differential equations and derive tractable approximate closed-form expressions for the equilibrium fees. Our analysis shows that the two-regime structure found in monopoly models persists under competition: pools alternate between raising fees to deter arbitrage and lowering fees to attract noise trading and increase volatility. Under competition, however, the switching boundary shifts from the oracle price to a weighted average of the oracle and competitors' exchange rates. Our numerical experiments show that, holding total liquidity fixed, an increase in the number of competing DEXs reduces execution slippage for strategic liquidity takers and lowers fee revenue per DEX. Finally, the effect on noise traders' slippage depends on market activity: they are worse off in low-activity markets but better off in high-activity ones.