In the intricate dance of modern commerce, where prices fluctuate with the speed of a click, a silent force is at play, potentially driving up costs for consumers. It’s not the backroom deals of old, but something far more subtle: the complex logic of pricing algorithms. For decades, the bedrock of consumer protection has been the prohibition of collusion – businesses conspiring to fix prices. The law, in its wisdom, assumed that if competitors were forbidden from agreeing on higher prices, they would naturally compete, leading to lower costs for everyone. This worked reasonably well for a long time, but the digital age has introduced a new player into the market: algorithms.
These aren’t the all-knowing, super-intelligent AI systems you might imagine. Many are far simpler learning algorithms designed to do one thing exceptionally well: optimize for profit by adjusting prices based on real-time market data. They observe demand, competitor actions, and inventory levels, and then tweak their prices accordingly. This constant adaptation, while often leading to efficiency, has also opened a Pandora’s Box of unintended consequences.
The Ghost of Collusion: Algorithms That Aren’t Talking, But Still Conspiring
The traditional regulatory approach, which hinges on proving explicit agreements between human sellers, is increasingly ill-equipped to handle this new landscape. As computer scientist Aaron Roth from the University of Pennsylvania aptly puts it, "The algorithms definitely are not having drinks with each other." Yet, a groundbreaking 2019 study demonstrated that algorithms, through a process of emergent learning, could achieve a form of tacit collusion. In a simulated market, two simple learning algorithms were pitted against each other. Over time, each algorithm learned to retaliate against price drops by its competitor. The retaliation wasn’t always proportional; it was often a drastic, disproportionate price reduction. The outcome? Both algorithms settled on higher prices, mutually enforced by the threat of devastating price wars.
This finding sent ripples through the economics and computer science communities. It highlighted the difficulty regulators face: how do you regulate behavior that mimics collusion but lacks any identifiable human agreement or intent? Roth himself acknowledges the challenge: "The message of our paper is it’s hard to figure out what to rule out."
The Game Theory Playbook: Understanding Strategic Interactions
To unravel these complex algorithmic behaviors, researchers are turning to game theory, a field that uses mathematical models to analyze strategic decision-making in competitive environments. It’s a powerful tool for dissecting how rational agents interact, and in this case, how pricing algorithms might learn to engage in non-competitive behavior.
Imagine a game like rock-paper-scissors. In this scenario, a learning algorithm represents a player’s strategy for choosing a move. Over many rounds, players learn and adapt. The ideal outcome in many games is an ‘equilibrium,’ where no player can improve their outcome by unilaterally changing their strategy. In rock-paper-scissors, the optimal strategy is to play randomly, choosing each option with equal probability.
However, learning algorithms shine when opponents deviate from this ideal. If one player consistently chooses rock, a learning algorithm can adapt and exploit this predictability by choosing paper more often. Game theorists call the missed opportunity to have played better, based on learned information, ‘regret.’
‘No-Regret’ Algorithms: A Promise of Fair Play?
Researchers have developed sophisticated learning algorithms designed to minimize ‘regret.’ These ‘no-swap-regret’ algorithms offer a crucial guarantee: no matter what the opponent does, the algorithm couldn’t have achieved a better outcome by simply swapping one of its past decisions for another. A significant theoretical breakthrough in 2000 proved that if two no-swap-regret algorithms compete against each other in any game, they will inevitably reach an equilibrium that mirrors the outcome of a single-round game. This is highly desirable because in single-round games, threats are impossible – there’s no future for a player to follow through on a threat. This suggested that two such algorithms competing in a market would always result in competitive prices, effectively eliminating the possibility of collusion.
When Benign Meets Unpredictable: The ‘Nonresponsive’ Strategy
This theoretical promise held for a while. A 2024 paper by Jason Hartline and his colleagues translated these findings to a market model, suggesting that dueling no-swap-regret algorithms would lead to competitive pricing. However, the real world of online marketplaces is more complex than just algorithms talking to themselves. What happens when a ‘no-regret’ algorithm encounters a different, seemingly benign strategy?
The answer, as discovered by Natalie Collina and Eshwar Arunachaleswaran, a graduate student working with Roth, is potentially problematic. They investigated the optimal strategy to play against a ‘no-swap-regret’ algorithm in a pricing game. The ‘best’ response, surprisingly, wasn’t about direct competition or threat, but a ‘nonresponsive’ strategy. This strategy involves picking moves (prices, in this context) based on a specific probability distribution, regardless of what the opponent does.
What Collina and Arunachaleswaran found was that the optimal probabilities for this nonresponsive strategy assigned surprisingly high weights to very high prices, alongside a range of lower prices. "To me, it was a complete surprise," Arunachaleswaran stated.
The Unintended Price Hikes: How ‘Dumb’ Strategies Can Lead to Expensive Outcomes
These nonresponsive strategies appear innocuous on the surface. They cannot issue explicit threats because they don’t react to their opponent’s actions. Yet, they can subtly influence learning algorithms to adopt higher prices. The nonresponsive player can then profit by occasionally undercutting its competitor. Initially, Collina and Arunachaleswaran believed this scenario was purely theoretical. They reasoned that any seller using a ‘no-swap-regret’ algorithm would quickly switch strategies upon realizing their competitor was profiting at their expense.
However, further analysis revealed a crucial insight. In their scenario, both algorithms were already in a state of equilibrium. Their profits were nearly equal and maximized under the condition that neither algorithm changed its fundamental strategy. Neither player had an incentive to deviate, leaving buyers stuck with inflated prices. The surprising part was that the specific probabilities weren’t as critical as the outcome itself. Many different probability assignments, when pitted against a ‘no-swap-regret’ algorithm, led to high prices. This is the hallmark of collusion, achieved without any explicit agreement or human oversight.
The Regulatory Conundrum: What’s the Solution?
This predicament leaves regulators in a challenging position. Aaron Roth admits he doesn’t have a simple answer. Banning ‘no-swap-regret’ algorithms outright seems counterproductive, as their widespread adoption would likely lead to lower prices. Yet, a simple nonresponsive strategy might be the most logical choice for a seller on a platform like Amazon, even if it carries the risk of regret for the seller if market conditions change dramatically.
Roth’s observation that "One way to have regret is just to be kind of dumb. Historically, that hasn’t been illegal" underscores the disconnect between economic outcomes and legal definitions. What looks like collusion from an economic standpoint might not meet the legal threshold for illegal activity if no intent or agreement can be proven.
Jason Hartline offers a more direct, albeit potentially controversial, solution: ban all pricing algorithms except for the favored ‘no-swap-regret’ algorithms. He believes this is practically achievable, citing work from his 2024 paper that proposes methods to verify an algorithm’s ‘no-swap-regret’ property without scrutinizing its source code.
Hartline argues that scenarios like the one described by Roth aren’t true algorithmic collusion because collusion, by definition, is a ‘two-way thing.’ It requires that a single player could choose not to collude. In his view, the nonresponsive strategy doesn’t inherently collude; it merely exploits the predictable behavior of another algorithm.
The Road Ahead: Uncharted Territory in Algorithmic Pricing
Regardless of the proposed solutions, the new research undeniably opens a complex discussion about the subtle ways algorithmic pricing can harm consumers. As economist Mallesh Pai of Rice University notes, "We still don’t understand nearly as much as we want. It’s an important question for our time." The challenge lies in developing regulatory frameworks that can adapt to the evolving sophistication of algorithms and ensure fair competition in the digital marketplace, even when the ‘conspirators’ are lines of code and the ‘threats’ are mathematical probabilities.
The original version of this story was published by Quanta Magazine, an editorially independent publication of the Simons Foundation. This rephrased article aims to make these complex ideas accessible and engaging for a wider audience.