Game Theory Explains How Algorithms Can Drive Up Prices

The original version of this story appeared in Quanta Magazine.

Imagine a town with two widget merchants. Customers prefer cheaper widgets, so the merchants must compete to set the lowest price. Unhappy with their meager profits, they meet one night in a smoke-filled tavern to discuss a secret plan: If they raise prices together instead of competing, they can both make more money. But that kind of intentional price-fixing, called collusion, has long been illegal. The widget merchants decide not to risk it, and everyone else gets to enjoy cheap widgets.

For well over a century, US law has followed this basic template: Ban those backroom deals, and fair prices should be maintained. These days, it’s not so simple. Across broad swaths of the economy, sellers increasingly rely on computer programs called learning algorithms, which repeatedly adjust prices in response to new data about the state of the market. 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, as it relies on finding explicit collusion. “The algorithms definitely are not having drinks with each other,” said Aaron Roth, a computer scientist at the University of Pennsylvania.

Yet a widely cited 2019 paper showed that algorithms could learn to collude tacitly, even when 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 cut prices—dropping its own price by some huge, disproportionate amount. The end result was high prices, backed up by mutual threat of a price war.

Implicit threats like this also underpin many cases of human collusion. So if you want to guarantee fair prices, why not just require sellers to use algorithms that are inherently incapable of expressing threats?

In a recent paper, Roth and four other computer scientists showed why this may not be enough. They proved that even seemingly benign algorithms that optimize for their own profit can sometimes yield bad outcomes for buyers. “You can still get high prices in ways that kind of look reasonable from the outside,” said Natalie Collina, a graduate student working with Roth who co-authored the new study.

Researchers don’t all agree on the implications of the finding—a lot hinges on how you define “reasonable.” But it reveals how subtle the questions around algorithmic pricing can get, and how hard it may be to regulate.