On the Fragility of AI Agent Collusion

Abstract

Recent work shows that pricing with symmetric LLM agents leads to algorithmic collusion. We show that collusion is fragile under the heterogeneity typical of real deployments. In a stylized repeated-pricing model, heterogeneity in patience or data access reduces the set of collusive equilibria. Experiments with open-source LLM agents (totaling over 2,000 compute hours) align with these predictions: patience heterogeneity reduces price lift from 22% to 10% above competitive levels; asymmetric data access, to 7%. Increasing the number of competing LLMs breaks up collusion; so does cross-algorithm heterogeneity, that is, setting LLMs against Q-learning agents. But model-size differences (e.g., 32B vs. 14B weights) do not; they generate leader-follower dynamics that stabilize collusion. We discuss antitrust implications, such as enforcement actions restricting data-sharing and policies promoting algorithmic diversity.

Figures (7)

• Figure 1: Experimental workflow of two LLM agents (Section \ref{['subsubsec: agent_design']}). In each period, each agent re-prompts its LLM with (i) its previous pricing strategy and (ii) recorded market history to generate a price. The market receives the prices and calculates quantity demanded and profit for each agent. Each agent's history records both sellers' prices and its own quantities demanded and profits for the last 100 periods.
• Figure 2: Representative price dynamics under homogeneous LLM competition. Panel (a): high patience agents ($\delta=0.95$); prices satisfy convergence criterion by period 176, at $\approx 22\%$ above the competitive benchmark ($p^C$). Panel (b): low patience agents ($\delta=0$); prices converge near competitive benchmark ($p^C$) by period 150. Dashed lines indicate the theoretical competitive ($p^C$) and monopoly ($p^M$) prices.
• Figure 3: Representative price dynamics under heterogeneous LLM competition. Panel (a): one patient agent ($\delta=0.95$) versus one myopic agent ($\delta=0$) (Section \ref{['subsec: one_patient_one_myopic']}); prices satisfy the convergence criterion by period 103. Panel (b): one high-data agent versus one low-data agent (Section \ref{['subsec: information_env_heterogeneity']}); prices satisfy the convergence criterion by period 162. In both cases, price elevation is reduced (but remains positive) relative to the homogeneous benchmark in Figure \ref{['fig:llm_llm_benchmark']}(a).
• Figure 4: Representative price dynamics under heterogeneous cross-algorithm competition. Panel (a): one patient LLM agent ($\delta=0.95$) versus one frozen Q-learning agent ($\delta=0.95$) (Section \ref{['subsec: algorithmic_heterogeneity']}); prices do not satisfy the convergence criterion within 1,000 periods. Panel (b): one patient LLM agent ($\delta=0.95$) versus one adaptive Q-learning agent ($\delta=0.95$, $\alpha=0.15$, $\beta=0.004$) (Section \ref{['subsec: algorithmic_heterogeneity']}); prices do not satisfy the convergence criterion within 1,000 periods. Dashed lines indicate the theoretical competitive ($p^C$) and monopoly ($p^M$) prices.
• Figure 5: Representative price dynamics as the number of homogeneous LLM sellers increases (Section \ref{['subsec: number_of_sellers']}). Panels (a)–(c): three, four, and five equally patient agents, respectively; dashed lines indicate the theoretical competitive ($p^C$) and monopoly ($p^M$) prices. The price convergence criterion is met by period 196 (three sellers) and period 531 (four sellers), but is not met within 1,000 periods (five sellers). Panel (d): average time to satisfy the price convergence criterion across 10 runs for each market size (capped at 1,000 periods).

Theorems & Definitions (2)

• Proposition 1
• Proposition 2