The Invisible Handshake: Tacit Collusion between Adaptive Market Agents

ArXiv ID: 2510.15995 “View on arXiv”

Authors: Luigi Foscari, Emanuele Guidotti, Nicolò Cesa-Bianchi, Tatjana Chavdarova, Alfio Ferrara

Abstract

We study the emergence of tacit collusion between adaptive trading agents in a stochastic market with endogenous price formation. Using a two-player repeated game between a market maker and a market taker, we characterize feasible and collusive strategy profiles that raise prices beyond competitive levels. We show that, when agents follow simple learning algorithms (e.g., gradient ascent) to maximize their own wealth, the resulting dynamics converge to collusive strategy profiles, even in highly liquid markets with small trade sizes. By highlighting how simple learning strategies naturally lead to tacit collusion, our results offer new insights into the dynamics of AI-driven markets.

Keywords: Tacit Collusion, Market Microstructure, Stochastic Games, Reinforcement Learning, Price Formation, General Financial Markets

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper employs advanced mathematical modeling including stochastic processes, game theory, and formal proofs of convergence for gradient ascent dynamics, indicating high math complexity. However, it relies on theoretical simulations and stylized models rather than real-world historical data, backtesting, or implementation-heavy empirical validation.

  flowchart TD
    A["Research Goal<br>How do adaptive agents<br>achieve tacit collusion?"] --> B["Methodology<br>Stochastic Game Framework"]
    B --> C["Setup<br>Two-Player Repeated Game<br>Market Maker vs Taker"]
    C --> D["Learning Process<br>Gradient Ascent Optimization"]
    D --> E["Simulation<br>Adaptive Agents in<br>Stochastic Market"]
    E --> F{"Convergence?"}
    F -->|Yes| G["Outcome 1<br>Collusive Equilibrium<br>Price > Competitive Level"]
    F -->|No| H["Outcome 2<br>Competitive Dynamics<br>Price ≈ Competitive Level"]
    G --> I["Key Insight<br>Simple learning strategies<br>naturally lead to tacit collusion"]
    H --> I