Algorithmic Collusion: How No-Swap Regret and Non-Responsive Pricing Shape High Prices

Two traditional rivals in the art market illustrate competition in the real world, then the discussion shifts to how modern pricing algorithms can raise prices without a backroom agreement. The Quanta podcast explains how learning pricing rules, such as no swap regret and non-responsive strategies, interact in markets, sometimes producing high-price equilibria even when no explicit collusion is present. The episode also cites a real-world DOJ case against Real Page to show algorithmic pricing can go wrong in practice, and it discusses regulatory and research directions aimed at understanding and mitigating these effects to protect consumers.

Introduction to Algorithmic Pricing and Collusion

The episode opens by framing price competition in traditional markets and then introduces a modern twist: prices are increasingly set by learning algorithms. The core question is how to adapt anti-collusion frameworks from law and economics to environments where prices are determined by data-driven software rather than human agreements. Ben Brewbaker explains that even seemingly innocent pricing programs can generate outcomes that look like collusion when they interact with other adaptive systems.

"Collusion in algorithms can be hard to define in terms of intent" - Ben Brewbaker, computer science writer.

What Collusion Means in the Algorithmic Era

In standard economic terms, collusion is anti-competitive behavior that raises prices. The challenge with algorithms is the nebulous notion of intent. The discussion distinguishes between human intent and the properties of the algorithms themselves, arguing that the focus should shift to the mathematical and strategic properties of the pricing rules and how they interact, rather than on hidden motives.

Kalina and Arunachaleswaran from UPenn explore how learning algorithms can create “collusion-like” outcomes through their interaction structures, even when each algorithm operates without explicit signaling or threat. This reframes the problem from one of intent to one of dynamics and equilibria.

No Swap Regret and Its Implications for Pricing

The conversation introduces no swap regret, a property where a learning algorithm never wishes it had replaced one action with another, across all possible swaps. When two no swap regret algorithms face off, they tend toward a favorable equilibrium that typically features competitive pricing and reduces the likelihood of traditional collusion.

"If two players use no swap regret algorithms, they reach a good equilibrium and collusion is not possible" - Ben Brewbaker.

Non-Responsive Strategies and Emergent High Prices

The discussion then considers non-responsive strategies, where one side assigns fixed probabilities to prices and does not react to the opponent's moves. Counterintuitively, pairing a non-responsive strategy with a no swap regret opponent can still produce high-price equilibria, illustrating how innocuous-looking rules can combine to the detriment of consumers.

"The best non-responsive strategy against a no swap regret opponent can still push prices high" - Natalie Kalina, UPenn graduate student.

Real-World Examples and Policy Questions

While the theoretical models are illuminating, there are real-world cases that show algorithmic pricing at work. The DOJ’s high-profile action against Real Page demonstrates how landlords using shared software can charge higher prices, with the algorithm acting as a tool rather than the sole culprit. The discussion emphasizes that policy responses must balance preventing harmful anti-competitive outcomes with preserving beneficial price optimization innovations.

"Algorithmic pricing can collide with anti-trust law in subtle ways" - Ben Brewbaker.

Future Research and Regulatory Considerations

The episode closes by acknowledging the unsettled policy landscape. Researchers advocate mapping algorithmic behaviors, exploring safe and unsafe classes of pricing rules, and considering regulatory approaches that can curb harmful emergent outcomes without stifling innovation. The overarching message is to develop a deeper, more systematic understanding of how interacting learning systems shape consumer prices.

"We need to map out these behaviors before bad things happen" - Ben Brewbaker.