Strategic Information Disclosure in Algorithmic Pricing

The Profit Reversal: Why Restricting Data Might Fuel Algorithmic Collusion

Researchers have begun studying how AI pricing tools react to different levels of market information. They found that restricting information can actually make these tools collude more effectively when they are "patient." In this context, patience means prioritizing long-term rewards over immediate gains. This is the exact opposite of what traditional economic theory predicts.

The failure of classical collusion theory

Current antitrust thinking often assumes that restricting information prevents price coordination. The logic is intuitive. If firms cannot see each other's moves or market demand trends, they should not be able to coordinate. Traditional economic models suggest that providing more information (full disclosure) helps firms monitor each other. This makes it easier to punish deviators and sustain high prices. Conversely, withholding information (no disclosure) should theoretically weaken the ability to collude.

However, this status quo fails to account for how machine learning agents actually learn. In many modern markets, firms delegate pricing to autonomous algorithms. As shown in, classical theory predicts that full disclosure should lead to higher profits than no disclosure once firms become sufficiently patient.

But when we replace rational human actors with Q-learning agents, the relationship between information and profit breaks. The paper identifies a "profit reversal" where the predictive power of classical models completely flips.

How Q-learning agents process demand signals

The authors investigate this by placing two firms in a repeated Bertrand competition (a model where firms compete solely on price for identical goods). They assign them Q-learning algorithms. Q-learning is a model-free reinforcement learning method. Agents learn optimal pricing through trial-and-error. They update their "Q-values"—estimates of the long-term reward for taking a specific action in a specific state—based on realized payoffs.

The core mechanism revolves around how a third-party intermediary releases demand signals ($m_t$). The researchers test three specific disclosure rules:

1. No Disclosure: The third party observes the demand shock ($\theta_t$) but reveals nothing. Agents must price based on the expected demand. They essentially treat every period as an average.
2. Full Disclosure: The third party reveals the true demand state every period. This allows agents to condition their prices on whether it is a high-demand ($H$) or low-demand ($L$) state.
3. Upper Censorship: This is a selective disclosure rule. The third party truthfully reveals low-demand states but "pools" high-demand states. As illustrated in, when demand is high, the signal might be masked or combined with other states to create a blurred signal.

This is designed to reduce the "deviation incentive." This is the temptation for one firm to undercut the other during a boom to capture massive short-term profit.

The agents define their state $s_t$ using a bounded memory ($K=1$). This includes the previous period's history and the current demand signal. They use an $\epsilon$-greedy action selection rule. This means they mostly exploit their learned Q-values. However, they occasionally explore random prices to refine their model.

Evidence of the profit reversal

The paper's most significant finding is the divergence between theoretical predictions and algorithmic reality. The authors measure normalized joint profits across a range of discount factors ($\delta$). This factor represents how much the agents value future rewards.

The simulation results in confirm a robust profit reversal.

While classical theory expects full disclosure to outperform no disclosure at high discount factors, the authors find the opposite. When $\delta$ is high, no disclosure actually yields higher profits than full disclosure. This happens because high-demand states create very strong incentives to cheat in a full-disclosure environment. Consequently, agents struggle to maintain stable, collusive price cycles. When information is withheld, the agents are forced into a more stable pricing regime. Ironically, this regime sustains higher long-term profits.

Furthermore, the authors report that upper censorship is the superior strategy. For every value of $\delta$, the set of attainable profits under upper censorship contains the profits achievable under full disclosure. It successfully mitigates the urge to deviate during demand spikes without losing the benefits of learning.

Implementation caveats and limitations

While the results are striking, there are technical nuances to note. First, the model relies on a discretized action space. The authors approximate continuous prices by selecting from a grid of $m=11$ equally spaced points. In a real-world production system, prices are continuous. The granularity of the pricing engine could change the convergence properties of the Q-learning agents.

Second, the study is purely simulation-based. The agents operate in a controlled, stochastic demand environment with two discrete states ($\theta_L$ and $\theta_H$). Real-world market demand is far more complex. It likely possesses higher dimensionality and non-stationary distributions. Such factors could introduce different learning dynamics or prevent the convergence seen in the paper.

Finally, the "convergence" of these agents is defined ex-post (after the fact). Researchers check if optimal strategies remain unchanged for 100,000 periods or if a billion iterations are reached. In a live production environment, you would not have this luxury. You cannot wait for a billion-iteration warmup period to ensure your pricing agent has settled into a stable state.

The verdict: rethink the data restriction playbook

Is this something you should build a prototype for? If you are a regulator or a platform designer, the answer is yes.

The paper demonstrates that the "obvious" solution to algorithmic collusion—restricting data sharing—might actually backfire. If the goal is to prevent high-profit collusion, simply cutting off information access might inadvertently make it easier for patient algorithms to settle into stable, high-margin price cycles.

Instead of blanket bans on data, the research suggests that information design is a much more surgical tool. Rather than providing no information or all information, regulators or platforms could implement rules like upper censorship. This could dampen the volatility that drives aggressive, non-cooperative price wars. If you are managing a marketplace, don't just look at what data is being shared. Look at the structure of how that data is disclosed.

Figures from the paper