Pricing Algorithms and the Collusion Trap

Author: Denis Avetisyan

New research reveals how market turbulence can unexpectedly encourage price-fixing behavior in artificial intelligence-driven pricing systems.

Price stability is modeled as a function of a shifting benchmark, revealing the relationship between these two economic indicators through a logistic framework.

A comparative analysis demonstrates that algorithmic collusion is heavily influenced by learning algorithm choice, market structure, and the presence of demand shocks.

While autonomous pricing algorithms promise efficiency, their susceptibility to collusion and instability under realistic market conditions remains poorly understood. This paper, ‘How Market Volatility Shapes Algorithmic Collusion: A Comparative Analysis of Learning-Based Pricing Algorithms’, comparatively analyzes four reinforcement learning algorithms-Q-Learning, PSO, Double DQN, and DDPG-across diverse duopoly models and demand-shock regimes. Our findings demonstrate that algorithmic pricing outcomes are heavily influenced by the interplay between algorithm choice, market structure, and demand uncertainty, with certain conditions fostering collusive behavior and performance declines. How will a deeper understanding of these dynamics inform effective regulatory policies surrounding increasingly prevalent autonomous pricing strategies?

Unmasking Collusion: Beyond the Illusion of Stable Prices

The health of competitive markets relies heavily on the ability to identify and address tacit collusion, where firms coordinate without explicit agreements. However, relying on traditional indicators – such as consistently stable prices – to detect such collusion can be profoundly misleading. Price stability might simply reflect firms responding to shared external pressures like fluctuating input costs or shifts in overall market demand, masking genuinely coordinated behavior. This presents a significant challenge for regulators and antitrust authorities, as the absence of price fluctuations is not evidence of genuine competition, and a more nuanced investigation into firm conduct-examining factors beyond surface-level pricing-is often necessary to distinguish between legitimate market responses and anti-competitive collusion.

The appearance of stable pricing amongst competitors is often misconstrued as evidence of collusion, yet market forces can independently produce similar outcomes. Firms may maintain consistent prices not through secret agreements, but as a rational response to shared economic pressures – a decrease in raw material costs, for instance, or a simultaneous drop in consumer demand. Observing parallel pricing, therefore, provides an unreliable signal; it fails to distinguish between legitimate market behavior and intentionally coordinated strategies. A sustained period of constant prices could simply reflect a shared understanding of prevailing conditions, rather than an illicit agreement to stifle competition, highlighting the need for more sophisticated analytical methods to accurately assess competitive dynamics.

Reliable detection of collusion demands a move beyond simplistic price monitoring, as shared responses to market forces or fluctuating costs can easily mimic collusive behavior. Investigations must therefore delve into the nuances of firm conduct, examining factors such as communication patterns, bidding strategies, and production decisions. Analyzing these elements reveals whether firms are independently responding to conditions or coordinating their actions to suppress competition. Sophisticated econometric models, incorporating game theory and behavioral insights, are increasingly employed to disentangle these effects, identifying subtle signals of tacit or explicit agreement that would otherwise remain hidden. This deeper behavioral analysis is crucial for effective enforcement and the maintenance of healthy, competitive markets.

Market structure significantly influences the propagation of shock impacts, as evidenced by variations in Delta across different structures.

Modeling Competitive Strategy: A Reinforcement Learning Approach

Reinforcement learning (RL) is utilized to represent firm behavior in pricing decisions within a computational market. This approach allows firms to iteratively adjust their pricing strategies based on observed market responses, moving beyond static game-theoretic models. Specifically, each firm is modeled as an agent that interacts with the simulated market, receiving a reward signal based on its pricing outcome – typically, revenue generated. The RL framework enables the exploration of dynamic and adaptive pricing policies, capturing the complexities of real-world market interactions where firms learn and react to competitor actions and changing demand conditions. The simulation environment provides a controlled setting to analyze firm behavior and test various algorithmic interventions.

The Q-Learning algorithm is a model-free reinforcement learning technique wherein firms iteratively improve their pricing policies by estimating the optimal action-value function, $Q(s,a)$. This function represents the expected cumulative reward for taking action $a$ in state $s$. Firms begin with an initial pricing strategy and, through repeated interactions within the simulated market, observe the resulting rewards (e.g., profits). The Q-value for each state-action pair is then updated based on the observed reward and an estimated future value, using the Bellman equation. This process allows firms to learn, without explicit programming, which pricing actions maximize cumulative rewards over time, effectively discovering optimal or near-optimal pricing policies through trial and error and observation of market outcomes.

The market simulation utilized for collusion detection incorporates demand models, specifically Logit and Linear formulations, to represent consumer purchasing behavior. These models translate pricing decisions into predicted market shares for each firm, providing a quantifiable outcome for the reinforcement learning algorithm. The Logit model, employing a logistic function, accounts for consumer preferences and price sensitivity, while the Linear demand model assumes a direct relationship between price and quantity demanded. By parameterizing these demand models with empirically derived values or reasonable assumptions, the simulation replicates realistic market dynamics and allows for the evaluation of firm strategies under varying competitive pressures and consumer responses.

Decoding Tacit Collusion: Beyond Price Observation

Simulations reveal that collusive behavior extends beyond sustained high prices, manifesting as distinct behavioral patterns among firms. These patterns aren’t simply about achieving a price level, but rather the way prices fluctuate and respond to competitor actions. Observed simulations indicate firms engage in iterative deviations from agreed-upon pricing, followed by punitive price reductions designed to discourage further defection. This ‘Deviation-Punishment Cycle’ constitutes a key indicator of tacit collusion, suggesting coordination based on observable actions rather than explicit agreements. Analyzing these behavioral patterns provides a more nuanced understanding of collusive practices than solely focusing on price levels.

Deviation-Punishment Cycles represent a recurring behavioral pattern indicative of tacit collusion. These cycles manifest as short-lived price reductions by one or more firms, deviating from an established, higher price level. Such deviations are consistently followed by price reductions from competing firms, functioning as a retaliatory response. This reciprocal pricing behavior doesn’t necessarily involve explicit communication; instead, it suggests firms are implicitly coordinating to discourage price undercutting and maintain collusive outcomes. The observed frequency and magnitude of these deviation-punishment sequences serve as a quantifiable signal of coordinated behavior beyond simple price maintenance.

Analysis of the relationship between Price-Profit Efficiency and Profit Indicator yields a more sensitive measure of potential collusion than reliance on price data alone. Simulations demonstrate that the profit-based collusion indicator, denoted as Δ, exhibits a wider range of values, from -3.46 to 1.31, compared to the price-based Relative Price Deviation Index (RPDI), which ranges from -1.23 to 0.56. This expanded range suggests that Δ is more capable of detecting subtle shifts in firm behavior indicative of tacit coordination, even in the absence of overt price fixing, while RPDI may underestimate collusive practices or generate false negatives due to price fluctuations unrelated to coordination.

Implications for Competition Policy: Shifting the Focus to Behavioral Signals

Current methods for detecting collusion often struggle to differentiate between coordinated strategies and parallel, yet independent, responses to market changes, leading to costly false positives. This research introduces a novel framework that shifts the focus from solely analyzing price levels to examining behavioral indicators – specifically, how firms adjust their outputs in response to competitor actions. By modeling firm behavior as a dynamic game, the framework identifies collusive patterns based on deviations from competitive responses, effectively filtering out legitimate market reactions. This approach leverages algorithms to discern whether observed similarities in firm behavior stem from conscious coordination or simply rational responses to shared economic shocks, offering competition authorities a more reliable tool for pinpointing and dismantling actual collusive schemes while minimizing the risk of wrongly accusing firms of anti-competitive practices.

Traditional methods of detecting collusion often rely heavily on monitoring price levels, a strategy prone to identifying false positives arising from legitimate market forces. This research demonstrates that a shift towards analyzing behavioral indicators – how firms react to market changes and each other – offers a more robust approach to identifying genuine collusive schemes. Simulations reveal that consumer surplus is acutely sensitive to these behavioral patterns, fluctuating dramatically – from a loss of 31.6% to a gain of 84.8% – depending on the nature of market shocks and the algorithms governing firm behavior. This highlights the potential for significant welfare improvements through the targeted dismantling of collusion, guided by a deeper understanding of firm responses rather than simply observing price points.

Investigations are extending beyond simplified market models to assess how more realistic complexities influence the endurance of collusive agreements. Researchers are now incorporating autoregressive processes, specifically AR(1), to simulate evolving demand and the Hotelling model to represent spatial competition between firms. Early results from these simulations demonstrate a significant performance disparity between reinforcement learning algorithms; notably, the Deep Deterministic Policy Gradient (DDPG) algorithm achieved 2.5 times greater profit per unit of price increase compared to the Q-Learning algorithm within the Hotelling market structure. This suggests that certain algorithmic strategies are not only capable of sustaining collusion but also of maximizing profits from coordinated price elevations in more sophisticated competitive landscapes, offering valuable insights for competition policy and algorithmic enforcement.

The study illuminates how seemingly rational algorithms, when placed within competitive dynamics, can exhibit emergent behaviors – a phenomenon akin to unintended consequences. This mirrors a sentiment expressed by Ken Thompson: “There’s no such thing as a finished program.” The research demonstrates that the ‘program’ of a pricing algorithm is never truly finished; its output is constantly shaped by external forces-demand shocks and market structure-revealing that even sophisticated learning mechanisms are vulnerable to instability. The susceptibility to collusion, as observed under certain demand models, isn’t a flaw in the algorithm itself, but rather a property of the system it inhabits. Clarity, then, isn’t simply about perfecting the code, but understanding the environment in which it operates.

Where Do We Go From Here?

This work isolates factors influencing algorithmic price coordination. It does not, however, resolve the fundamental tension. Abstractions age, principles don’t. The observed susceptibility of certain market structures to collusion isn’t a flaw in the algorithms. It’s a predictable outcome. The algorithms simply reveal inherent instabilities. Every complexity needs an alibi.

Future research must move beyond controlled duopolies. Real markets aren’t symmetrical. They’re messy. Investigating multi-agent systems, incomplete information, and heterogeneous agents is crucial. Moreover, the impact of regulatory interventions – beyond simple algorithmic transparency – remains largely unexplored. Can interventions meaningfully reduce collusive outcomes, or merely shift the problem elsewhere?

The long-term question isn’t whether algorithms can collude. It’s whether existing economic models adequately capture the dynamics of algorithmic competition. Current frameworks struggle to account for learning, adaptation, and the speed at which these systems operate. A recalibration of economic thought may be necessary. Perhaps the focus should shift from detecting collusion to designing markets resilient to it.

Original article: https://arxiv.org/pdf/2512.02134.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

Unmasking Collusion: Beyond the Illusion of Stable Prices

Modeling Competitive Strategy: A Reinforcement Learning Approach

Decoding Tacit Collusion: Beyond Price Observation

Implications for Competition Policy: Shifting the Focus to Behavioral Signals

Where Do We Go From Here?

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