AI agents are increasingly deployed in ecosystems where they repeatedly interact not only with each other but also with humans. In this work, we study these human-AI ecosystems from a theoretical perspective, focusing on the classical framework of repeated pricing games. In our stylized model, the AI agents play equilibrium strategies, and one or more humans manually perform the pricing task instead of adopting an AI agent, thereby defecting to a no-regret strategy. Motivated by how populations of AI agents can sustain supracompetitive prices, we investigate whether high prices persist under such defections. Our main finding is that even a single human defection can destabilize collusion and drive down prices, and multiple defections push prices even closer to competitive levels. We further show how the nature of collusion changes under defection-aware AI agents. Taken together, our results characterize when algorithmic collusion is fragile--and when it persists--in mixed ecosystems of AI agents and humans.

The rise of autonomous pricing systems has sparked growing concern over algorithmic collusion in markets from retail to housing. This paper examines controlled information quality as an ex ante policy lever: by reducing the fidelity of data that pricing algorithms draw on, regulators can frustrate collusion before supracompetitive prices emerge. We show, first, that information quality is the central driver of competitive outcomes, shaping prices, profits, and consumer welfare. Second, we demonstrate that collusion can be slowed or destabilized by injecting carefully calibrated noise into pooled market data, yielding a feasibility region where intervention disrupts cartels without undermining legitimate pricing. Together, these results highlight information control as a lightweight yet practical lever to blunt digital collusion at its source.

Algorithmic pricing is increasingly shaping market competition, raising concerns about its potential to compromise competitive dynamics. While prior work has shown that reinforcement learning (RL)-based pricing algorithms can lead to tacit collusion, less attention has been given to the role of macroeconomic factors in shaping these dynamics. This study examines the role of inflation in influencing algorithmic collusion within competitive markets. By incorporating inflation shocks into a RL-based pricing model, we analyze whether agents adapt their strategies to sustain supra-competitive profits. Our findings indicate that inflation reduces market competitiveness by fostering implicit coordination among agents, even without direct collusion. However, despite achieving sustained higher profitability, agents fail to develop robust punishment mechanisms to deter deviations from equilibrium strategies. The results suggest that inflation amplifies non-competitive dynamics in algorithmic pricing, emphasizing the need for regulatory oversight in markets where AI-driven pricing is prevalent.

Algorithmic agents are used in a variety of competitive decision settings, notably in making pricing decisions in contexts that range from online retail to residential home rentals. Business managers, algorithm designers, legal scholars, and regulators alike are all starting to consider the ramifications of "algorithmic collusion." We study the emergent behavior of multi-armed bandit machine learning algorithms used in situations where agents are competing, but they have no information about the strategic interaction they are engaged in. Using a general-form repeated Prisoner's Dilemma game, agents engage in online learning with no prior model of game structure and no knowledge of competitors' states or actions (e.g., no observation of competing prices). We show that these context-free bandits, with no knowledge of opponents' choices or outcomes, still will consistently learn collusive behavior - what we call "naive collusion." We primarily study this system through an analytical model and examine perturbations to the model through simulations. Our findings have several notable implications for regulators. First, calls to limit algorithms from conditioning on competitors' prices are insufficient to prevent algorithmic collusion. This is a direct result of collusion arising even in the naive setting. Second, symmetry in algorithms can increase collusion potential. This highlights a new, simple mechanism for "hub-and-spoke" algorithmic collusion. A central distributor need not imbue its algorithm with supra-competitive tendencies for apparent collusion to arise; it can simply arise by using certain (common) machine learning algorithms. Finally, we highlight that collusive outcomes depend starkly on the specific algorithm being used, and we highlight market and algorithmic conditions under which it will be unknown a priori whether collusion occurs.

Two issues of algorithmic collusion are addressed in this paper. First, we show that in a general class of symmetric games, including Prisoner's Dilemma, Bertrand competition, and any (nonlinear) mixture of first and second price auction, only (strict) Nash Equilibrium (NE) is stochastically stable. Therefore, the tacit collusion is driven by failure to learn NE due to insufficient learning, instead of learning some strategies to sustain collusive outcomes. Second, we study how algorithms adapt to collusion in real simulations with insufficient learning. Extensive explorations in early stages and discount factors inflates the Q-value, which interrupts the sequential and alternative price undercut and leads to bilateral rebound. The process is iterated, making the price curves like Edgeworth cycles. When both exploration rate and Q-value decrease, algorithms may bilaterally rebound to relatively high common price level by coincidence, and then get stuck. Finally, we accommodate our reasoning to simulation outcomes in the literature, including optimistic initialization, market design and algorithm design.

Algorithmic collusion refers to the market phenomenon that when two or more competing parties use algorithms to assist decision-making, over time it may unintentionally lead to collusion instead of the typical Nash equilibrium. For example, consider two firms setting prices for their products, which are competing for customers. In the classic Bertrand competition, when the demand functions (how the market demand for either product depends on the prices of itself and the competitor) for both products are common knowledge, the firms may charge $10 in the (symmetric) Nash equilibrium. On the other hand, when the demand functions are unknown initially, the two firms may deploy reinforcement learning algorithms to learn the demand functions and maximize profits simultaneously. Algorithmic collusion emerges when the long-term outcome of the algorithms is an equilibrium in which both firms charge more than $10 for the products. It has been shown in the recent literature that algorithmic collusion is possible in theoretical and experimental settings [8, 15, 26].

The rise of algorithmic pricing raises concerns of algorithmic collusion. We conduct experiments with algorithmic pricing agents based on Large Language Models (LLMs), and specifically GPT-4. We find that (1) LLM-based agents are adept at pricing tasks, (2) LLM-based pricing agents autonomously collude in oligopoly settings to the detriment of consumers, and (3) variation in seemingly innocuous phrases in LLM instructions ("prompts") may increase collusion. These results extend to auction settings. Our findings underscore the need for antitrust regulation regarding algorithmic pricing, and uncover regulatory challenges unique to LLM-based pricing agents.

Fair machine learning research has been primarily concerned with classification tasks that result in discrimination. However, as machine learning algorithms are applied in new contexts the harms and injustices that result are qualitatively different than those presently studied. The existing research paradigm in machine learning which develops metrics and definitions of fairness cannot account for these qualitatively different types of injustice. One example of this is the problem of algorithmic collusion and market fairness. The negative consequences of algorithmic collusion affect all consumers, not only particular members of a protected class. Drawing on this case study, I propose an ethical framework for researchers and practitioners in machine learning seeking to develop and apply fairness metrics that extends to new domains. This contribution ties the development of formal metrics of fairness to specifically scoped normative principles. This enables fairness metrics to reflect different concerns from discrimination. I conclude with the limitations of my proposal and discuss promising avenues for future research.

Recent academic research has extensively examined algorithmic collusion resulting from the utilization of artificial intelligence (AI)-based dynamic pricing algorithms. Nevertheless, e-commerce platforms employ recommendation algorithms to allocate exposure to various products, and this important aspect has been largely overlooked in previous studies on algorithmic collusion. Our study bridges this important gap in the literature and examines how recommendation algorithms can determine the competitive or collusive dynamics of AI-based pricing algorithms. Specifically, two commonly deployed recommendation algorithms are examined: (i) a recommender system that aims to maximize the sellers' total profit (profit-based recommender system) and (ii) a recommender system that aims to maximize the demand for products sold on the platform (demand-based recommender system). We construct a repeated game framework that incorporates both pricing algorithms adopted by sellers and the platform's recommender system. Subsequently, we conduct experiments to observe price dynamics and ascertain the final equilibrium. Experimental results reveal that a profit-based recommender system intensifies algorithmic collusion among sellers due to its congruence with sellers' profit-maximizing objectives. Conversely, a demand-based recommender system fosters price competition among sellers and results in a lower price, owing to its misalignment with sellers' goals. Extended analyses suggest the robustness of our findings in various market scenarios. Overall, we highlight the importance of platforms' recommender systems in delineating the competitive structure of the digital marketplace, providing important insights for market participants and corresponding policymakers.

The prospect of collusive agreements being stabilized via the use of pricing algorithms is widely discussed by antitrust experts and economists. However, the literature is often lacking the perspective of computer scientists, and seems to regularly overestimate the applicability of recent progress in machine learning to the complex coordination problem firms face in forming cartels. Similarly, modelling results supporting the possibility of collusion by learning algorithms often use simple market simulations which allows them to use simple algorithms that do not produce many of the problems machine learning practitioners have to deal with in real-world problems, which could prove to be particularly detrimental to learning collusive agreements. After critically reviewing the literature on algorithmic collusion, and connecting it to results from computer science, we find that while it is likely too early to adapt antitrust law to be able to deal with self-learning algorithms colluding in real markets, other forms of algorithmic collusion, such as hub-and-spoke arrangements facilitated by centralized pricing algorithms might already warrant legislative action.