Game Theory Explains How Algorithms Can Drive Up Prices

The original version of this story appeared in Quanta Magazine.

Imagine a town with two gadget sellers. Customers prefer cheaper widgets, so merchants must compete to set the lowest price. Dissatisfied with their meager profits, they meet one evening in a smoky tavern to discuss a secret plan: if they raise prices together instead of competing with each other, they can both make more money. But this type of intentional price fixing, called collusion, has long been illegal. Widget sellers decide not to take risks and everyone can benefit from cheap widgets.

For more than a century, American law has followed this basic pattern: prohibiting these backroom deals and maintaining fair prices. Nowadays, it’s not that simple. Across large swaths of the economy, sellers increasingly rely on computer programs called learning algorithms, which repeatedly adjust prices in response to new data about market conditions. These are often much simpler than the “deep learning” algorithms that power modern artificial intelligence, but they can still be prone to unexpected behavior.

So how can regulators ensure that algorithms set fair prices? Their traditional approach won’t work because it relies on discovering explicit collusion. “Algorithms definitely don’t drink among themselves,” said Aaron Roth, a computer scientist at the University of Pennsylvania.

Yet a widely cited 2019 paper showed that algorithms could learn to get along tacitly, even if they weren’t programmed to do so. A team of researchers pitted two copies of a simple learning algorithm against each other in a simulated market, then let them explore different strategies for increasing their profits. Over time, each algorithm learned, through trial and error, to retaliate when the other lowered prices, by lowering its own price by a huge and disproportionate amount. The end result was high prices, supported by the mutual threat of a price war.

Aaron Roth suspects that the pitfalls of algorithmic pricing may not have a simple solution. “The message from our paper is that it is difficult to know what to exclude,” he said.

Photography: Courtesy of Aaron Roth

Such implicit threats also underlie many cases of human collusion. So, if we want to ensure fair prices, why not simply require sellers to use algorithms that are inherently incapable of expressing threats?

In a recent paper, Roth and four other computer scientists showed why that might not be enough. They proved that even seemingly harmless algorithms that optimize for their own profit can sometimes give buyers poor results. “You can still get high prices in a way that looks reasonable from the outside,” said Natalie Collina, a graduate student working with Roth and co-author of the new study.

Researchers don’t all agree on the implications of these findings – it largely depends on how you define “reasonable.” But it reveals how subtle the issues around algorithmic pricing can become and how difficult it can be to regulate.