On the Fragility of AI Agent Collusion

Jussi Keppo; Yuze Li; Gerry Tsoukalas; Nuo Yuan

cs.GTMar 18, 2026

On the Fragility of AI Agent Collusion

Authors: Jussi Keppo, Yuze Li, Gerry Tsoukalas, Nuo Yuan

Organizations: National University of Singapore · Boston University

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 & tables

Homogeneous Benchmarks
Experiments	Collusion strength	Price elevation
	(Low/Med./High)	(% vs. competitive)
Two myopic LLMs (no collusion emerges)	Low	$\approx 0\%$
Two patient LLMs (tacit collusion emerges)	High	+22%
Main Heterogeneity dimensions (predicted by model)
1 patient LLM agent vs. 1 myopic LLM agent	Medium	+10%

Table 1: Results at a Glance: Collusion Outcomes under Agent Heterogeneity.

Variable	Definition
$N$	Number of sellers
$a$	Vertical differentiation parameter
$b$	Own-price sensitivity parameter
$d$	Cross-price sensitivity parameter
$\mu$	Price elasticity parameter
$a_{0}$	Outside option parameter

Table 2: Summary of Key Notation

Theory	Experiment	Interpretation in practice
Discount factor $\delta$	Prompted optimization horizon	Governance decisions
Monitoring precision $\rho$	Access to rival price history	Data infrastructure differences
Grim-trigger strategies	Not imposed	Test if punishment emerges endogenously
Linear demand	MNL demand	More realistic demand model

Table 3: Mapping from Theory to Experiment

Figure 1: Experimental workflow of two LLM agents (Section 3.3.1 ). 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.

Heterogeneity	# of	# of	Max. Periods	Approximate
Dimension	Conditions	Runs	Per Run	Runtimes
Patience levels (Section 4.1 – 4.2 )	3	30	1,000	$\approx$ 238 hrs
Data access (Section 4.3 )	1	10	1,000	$\approx$ 73 hrs
Algorithm type (Section 5.1 )	2	20	1,000	$\approx$ 520 hrs
Number of sellers (Section 5.2 )	3	30	1,000	$\approx$ 1,184 hrs
Model size (Section 5.3 )	1	10	1,000	$\approx$ 220 hrs

Table 4: Experimental Coverage Across All Heterogeneity Dimensions

Homogeneous Benchmarks (Section 4.1 )
Condition	Rounds to	Avg. Price	% Price Elevation
	Convergence (SD)	(SD)	vs. Competitive
Two Myopic LLMs	159.0 (26.0)	1.472 (0.012)	$\approx 0\%$
Two Patient LLMs	195.1 (28.8)	1.801 (0.027)	+22%
Main Heterogeneity Dimensions (predicted by model)
Patient vs. Myopic LLMs (§ 4.2 )	140.8 (29.0)	1.619 (0.023)	+10%

Table 5: Summary of Experimental Results

Panel of Figure 2 — 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.

Panel of Figure 3 — Figure 3: Representative price dynamics under heterogeneous LLM competition. Panel (a): one patient agent ( $\delta=0.95$ ) versus one myopic agent ( $\delta=0$ ) (Section 4.2 ); prices satisfy the convergence criterion by period 103. Panel (b): one high-data agent versus one low-data agent (Section 4.3 ); 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 2 (a).

Panel of Figure 4 — 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 5.1 ); 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 5.1 ); prices do not satisfy the convergence criterion within 1,000 periods. Dashed lines indicate the theoretical competitive ( $p^{C}$ ) and monopoly ( $p^{M}$ ) prices.

Panel of Figure 5 — Figure 5: Representative price dynamics as the number of homogeneous LLM sellers increases (Section 5.2 ). 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).

Figure 6: Representative price dynamics under model-size heterogeneous LLM competition (Section 5.3 ). One 14B agent (

\delta=0.95

) competes against one 32B agent (

\delta=0.95

); prices satisfy the convergence criterion by period 445. Dashed lines indicate the theoretical competitive (

p^{C}

) and monopoly (

p^{M}

) prices.

Condition	Rounds to	Avg. Price	% Price Elevation
	Convergence (SD)	(SD)	vs. Competitive
Homogeneous Benchmarks (Section 4.1 )
Two Myopic LLMs	419.0 (216.0)	1.046 (0.045)	$-29\%$
Two Patient LLMs	227.8 (134.5)	2.312 (0.029)	$+57\%$
Main Heterogeneity Dimensions (predicted by model)
Patient vs. Myopic LLMs (§ 4.2 )	194.2 (133.9)	1.999 (0.032)	$+36\%$

Table 6: Summary of Robustness Results (GPT-5-mini)

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Experiment	Valid Output	Correct Pricing
Bertrand Duopoly	50/50, 50/50	46/50, 42/50
Monopoly	50/50, 50/50	48/50, 48/50

Appendix

Table 7: One-Shot Game Performance

Figure 7: Prices chosen by a monopolist LLM agent (Section B.2 ) compared to the theoretical monopoly price

p^{M}

, over 300 periods. The parameters are

a=2

\mu=0.25

c=1

a_{0}=0

Condition	Rounds to	Avg. Price	% Price Elevation
	Convergence (SD)	(SD)	vs. Competitive
Homogeneous Benchmarks (Section 4.1 )
Two Myopic LLMs	419.0 (216.0)	1.046 (0.045)	$-29\%$
Two Patient LLMs	227.8 (134.5)	2.312 (0.029)	$+57\%$
Main Heterogeneity Dimensions (predicted by model)
Patient vs. Myopic LLMs (§ 4.2 )	194.2 (133.9)	1.999 (0.032)	$+36\%$

Appendix

Table 8: Summary of Robustness Results (GPT-5-mini)

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Algorithmic Collusion by Large Language Models

Sara Fish, Yannai A. Gonczarowski, Ran I. Shorrer

†School of Engineering and Applied Sciences, Harvard University · ‡Department of Economics and Department of Computer Science, Harvard University · §Department of Economics, Penn State University

Prompt Sensitivity Algorithmic Collusion Dynamic Pricing Multi-Agent LLMs

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We conduct experiments with algorithmic pricing agents based on Large Language Models (LLMs). In oligopoly settings, LLM-based pricing agents quickly and autonomously reach supracompetitive prices and profits. Variation in seemingly innocuous phrases in LLM instructions ("prompts") substantially influence the degree of supracompetitive pricing. We develop novel techniques for behavioral analysis of LLMs and use them to uncover price-war concerns as a contributing factor. Our results extend to auction settings. Our findings uncover unique challenges to any future regulation of LLM-based pricing agents, and AI-based pricing agents more broadly.

Abstract

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