Competition between DEXs through Dynamic Fees

Battle Count: 77

Highly relevant for DeFi market making, AMM fee optimization, and multi-venue order routing strategies. The paper provides actionable insights for liquidity providers setting dynamic fees in competitive environments and for strategic traders routing orders across multiple DEXs. The two-regime fee structure and weighted-average switching boundary have direct implications for algorithmic execution in DeFi. However, it is more protocol-design oriented than traditional quantitative trading strategy development.

High complexity due to: (1) coupled system of HJB PDEs on multi-dimensional inventory grids, (2) matrix exponential computations for closed-form solutions, (3) stochastic simulation of controlled point processes with exponential intensities, (4) Nash equilibrium computation requiring iterative solution of coupled optimization problems, (5) numerical discretization of continuous-time models on finite grids. The linear approximation of fees reduces practical implementation complexity significantly.

The paper provides a GitHub repository with implementation details and numerical checks. The model is fully specified with explicit parameters, grid structures, and PDE formulations. However, the mathematical derivations involve approximations (negligible cross-inventory effects, treating oracle price as parameter) that require careful implementation. The code repository at https://github.com/leonardobaggiani/amm-fees-competition supports reproducibility.