Paper: arXiv 2611.01799

Authors: Irene Aldridge

Abstract

Automated markets increasingly route order flow from learning trading agents through automated market makers (AMMs). We model trader archetypes as AI agents defined by their reward functions and analyze the feedback they create on a constant-product AMM. Herd-dominated and arbitrage-dominated markets of equal size have identical return distributions and turnover, so no rule based on volatility, value-at-risk, stress frequency, or volume can tell them apart; yet their stress episodes differ in length by a factor unbounded in the feedback-to-noise ratio $β/s$. Serial statistics identify the feedback sign from $Θ((s/β)^2\log(1/δ))$ observations, and this rate is tight. When agents trade together, profit-seeking agents ride herds rather than lean against them, leading to all-or-nothing participation. Spread-earning market makers restore stability but make liquidity fragile, with discontinuous collapse and hysteresis; maker–taker pricing, not a uniform fee, is the effective instrument.

Complexity vs Empirical Score

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

Why this score: This paper presents a highly mathematical and theoretical model of automated markets and AI agents, demonstrating strong novelty in its analytical findings. While it connects to companion empirical work, the paper itself is primarily theoretical with limited direct empirical validation or backtesting details within the provided excerpt. The mathematical derivations are dense and rigorous, but the empirical rigor is not explicitly detailed.

Research Flowchart

  flowchart TD
    A[Research Goal: Analyze Feedback of AI Agents on AMMs] --> B{Methodology: Model Trader Archetypes as AI Agents};
    B --> C[Data/Inputs: Constant-Product AMM, Agent Reward Functions];
    C --> D{Computational Process: Simulate Herd-dominated vs. Arbitrage-dominated Markets};
    D --> E[Key Finding 1: Identical Return Distributions & Turnover for Herd/Arbitrage Markets];
    E --> F[Key Finding 2: Stress Episode Length Differs Significantly (unbounded in β/s)];
    F --> G[Key Finding 3: Serial Statistics Identify Feedback Sign (Θ((s/β)^2log(1/δ)) observations)];
    G --> H[Key Finding 4: Profit-seeking agents ride herds, leading to all-or-nothing participation];
    H --> I[Key Finding 5: Spread-earning MMs restore stability but create fragile liquidity (discontinuous collapse/hysteresis)];
    I --> J[Key Finding 6: Maker-taker pricing is effective instrument, not uniform fee];