A Dynamic Equilibrium Model for Automated Market Makers

Abstract: Automated Market Makers (AMMs) are a central component of decentralized exchanges, yet their equilibrium foundations and microeconomic mechanisms remain incompletely understood. This paper develops a dynamic equilibrium framework for Constant Function Market Makers (CFMMs) that formalizes the strategic interaction between arbitrageurs and liquidity providers (LPs) over time. We make three main contributions. First, we derive and empirically validate an intrinsic buy-sell asymmetry in CFMM price impact. Even in the absence of directional price movements, the geometric structure of constant product AMMs implies systematically different execution costs for buying and selling, a prediction that we confirm using on-chain transaction data. Second, we characterize the optimization problems of arbitrageurs and LPs in closed form, incorporating slippage and fees. In a baseline environment with only informed arbitrageurs, we show that providing liquidity is strictly dominated for LPs: arbitrage-driven price corrections generate negative jump returns that cannot be offset by fees, yielding a degenerate equilibrium with minimal liquidity provision. Third, motivated by empirical evidence, we extend the model to include agent heterogeneity, endogenous gas fees, and time varying volatility. In this extended environment, noise trading, arbitrage races, and execution costs jointly determine LP returns, giving rise to an interior equilibrium in which optimal liquidity provision is non-monotonic in volatility and exhibits a hump-shaped relationship. Overall, this paper builds a dynamic equilibrium model calibrated on extensive data that characterize the complex interaction between informed arbitrageurs, noise traders, and liquidity providers.