Paper: arXiv 2503.22502

Abstract

We find the equilibrium contract that an automated market maker (AMM) offers to their strategic liquidity providers (LPs) in order to maximize the order flow that gets processed by the venue. Our model is formulated as a leader-follower stochastic game, where the venue is the leader and a representative LP is the follower. We derive approximate closed-form equilibrium solutions to the stochastic game and analyze the reward structure. Our findings suggest that under the equilibrium contract, LPs have incentives to add liquidity to the pool only when higher liquidity on average attracts more noise trading. The equilibrium contract depends on the external price, the pool reference price, and the pool reserves. Our framework offers insights into AMM design for maximizing order flow while ensuring LP profitability.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper employs advanced stochastic control and game theory (leader-follower stochastic game) with integral transforms and intensity processes to derive approximate closed-form equilibrium solutions, indicating high mathematical density. However, it lacks backtesting results, real-world data implementation details, or trading performance metrics, relying instead on theoretical modeling and synthetic simulation descriptions.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Find equilibrium contract for AMM<br>to maximize order flow & LP profit"] --> B["Methodology: Leader-Follower Stochastic Game"]
  
  B --> C["Game Setup & Data Inputs"]
  C --> C1["AMM (Leader): Fee & Reserve Policy"]
  C --> C2["LP (Follower): Liquidity Decision"]
  C --> C3["Noise Trading: Arrival Rate & Size"]
  
  C --> D["Computational Process"]
  D --> D1["Backward Induction: LP's Stochastic Control"]
  D --> D2["Forward Optimization: AMM's Contraction Mapping"]
  D --> D3["Fixed Point Iteration for Equilibrium"]
  
  D --> E["Key Findings & Outcomes"]
  E --> E1["Equilibrium Contract<br>Depends on: External Price, Pool Reference, Reserves"]
  E --> E2["LP Incentives<br>Liquidity added only when it attracts order flow"]
  E --> E3["Design Implication<br>Optimal AMM design balances fees and liquidity depth"]

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12 of 95 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.