Citation

Zang, C., Wang, Z., Zhang, W. “A Dynamic Equilibrium Model for Automated Market Makers.” arXiv:2603.08603v1 [econ.GN] (Mar 9, 2026). Submitted to ACM EC ‘26.

Core Contributions

  1. Intrinsic buy-sell asymmetry: Proves that even without directional price movements, constant-product AMMs have different execution costs for buying vs. selling (due to geometric structure of the bonding curve). Confirmed with on-chain data.

  2. Degenerate equilibrium without heterogeneity: In a baseline environment with only informed arbitrageurs, providing LP liquidity is strictly dominated — arbitrage-driven corrections generate negative jump returns that fee income cannot offset. Result: minimal liquidity provision at equilibrium.

  3. Extended model with heterogeneity: Including noise traders, endogenous gas fees, and time-varying volatility gives an interior equilibrium where:

    • Optimal liquidity provision is non-monotonic in volatility
    • Shows a hump-shaped relationship with volatility
    • Noise trading and execution costs jointly determine LP returns

Key Results for MEV Research

Arbitrageur-LP Dynamics

  • Without noise trading, arbitrageurs always extract value from LPs
  • The equilibrium LP position is driven toward zero — LPs are rational to exit
  • This formalizes why AMMs with only informed traders (no retail flow) fail

The Role of Noise Traders

  • Noise traders (uninformed retail traders) are essential to LP viability
  • Their presence creates fee income that partially offsets LVR
  • MEV strategies that drive away retail flow (bad UX, sandwich attacks) reduce LP viability

Gas Fees in the Model

  • Endogenous gas fees enter as a cost for arbitrageurs
  • Higher gas → less frequent arb → better LP returns in steady state
  • Encrypted mempools that prevent arb also reduce LP adversarial selection costs

Connection to LVR

This paper provides a dynamic game-theoretic foundation for LVR:

  • LVR measures the LP cost in static models (σ²/8f per unit capital)
  • This paper shows how LVR costs and fee income balance in dynamic equilibrium
  • The hump-shaped LP return curve implies: very low volatility (low LVR, low fees) and very high volatility (high LVR, even higher losses) both reduce LP profits; medium volatility is optimal

Relationship to PropAMMs

  • In the baseline model, propAMMs (oracle-first pricing) solve the LVR problem by eliminating informed arbitrage opportunities
  • But the paper shows propAMMs need noise trading to generate LP returns — fee income must come from somewhere
  • PropAMMs shift LP income from fee spread to pure transaction fees, which works only if trading volume exists