Decentralized exchanges (DEXs) compete for trading volume by adjusting their fees. Each pool faces a fundamental tension: high fees earn more per trade but attract fewer traders; low fees attract volume but earn less. In a monopoly model, the optimal fee alternates between two regimes — raising fees to deter informed arbitrageurs when the pool price diverges from the oracle, and lowering fees to attract uninformed “noise” traders when prices align.
Baggiani, Herdegen, and Sanchez-Betancourt (arXiv:2603.09669) extend this to competition between multiple DEXs and find an approximate Nash equilibrium. The two-regime structure survives competition: pools still alternate between deterring arbitrage and courting noise trading. But competition shifts the switching boundary. In monopoly, the regime switch happens at the oracle price. In competition, it happens at a weighted average that incorporates competitors' fee rates. Each pool's strategy must account for what the others are charging.
The competitive equilibrium is described by coupled partial differential equations — each pool's optimal fee depends on the other pools' fees, which depend on the first pool's fee. The authors provide closed-form approximations that capture the essential structure: competition reduces execution slippage for sophisticated traders (who can route to the lowest-fee pool) and reduces per-exchange revenue when total liquidity is fixed.
The asymmetric effect on trader types is the subtlety. Noise traders — those trading for reasons unrelated to price information — face worse slippage in inactive markets (where competition for their volume is low) but better slippage in active markets (where pools compete aggressively for any volume). Sophisticated traders benefit uniformly because they can always choose the cheapest venue.