Competition between DEXs through Dynamic Fees

Paper: arXiv 2603.09669

Authors: Leonardo Baggiani, Martin Herdegen, Leandro Sanchez-Betancourt

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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous game-theoretic framework using coupled stochastic differential equations and dynamic programming to solve for dynamic equilibrium trading fees across competing decentralized exchanges (DEXs). While highly advanced mathematically and conceptually original, its empirical validation is limited to stylized numerical simulations rather than real historical market backtesting.

Research Flowchart

  flowchart TD
    A[Research Goal: Analyze Competition Between DEXs via Dynamic Fees] --> B[Model Formulation: Multi-DEX Game for Order Flow]
    B --> C[Methodology: Derive Coupled System of Partial Differential Equations]
    C --> D[Analytical Process: Solve System for Approximate Closed-Form Fees]
    D --> E[Numerical Experiments: Fixed Liquidity across Competing DEXs]
    E --> F[Key Outcome 1: Fees Switch Based on Weighted Average of Oracle & Competitor Rates]
    E --> G[Key Outcome 2: More DEXs Lower Slippage for Strategic Takers & Fee Revenue/DEX]
    E --> H[Key Outcome 3: Noise Trader Slippage Worsens in Low Activity, Improves in High]

Cited References (29)

1. Optimal Dynamic Fees in Automated Market Makers — → 2506.02869
2. The need for fees at a dex: How increases in fees can increase dex trading volume (2022)
3. Automated Market Making and Arbitrage Profits in the Presence of Fees — → 2305.14604
4. Automated market making and loss-versus-rebalancing (2022) — link
5. Quantifying loss in automated market makers (2022)
6. Optimal Fees for Geometric Mean Market Makers (2021)
7. Optimal Design of Automated Market Makers on Decentralized Exchanges — → 2404.13291
8. The Price of Liquidity: Implied Volatility of Automated Market Maker Fees — → 2509.23222

13 of 29 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.