UC Berkeley Researchers Offer a Smarter Way to Price With Stability and Impact in Mind

With inflation, tariffs, and shifting consumer habits, setting the right price has never been more complicated or more crucial. But new research from UC Berkeley’s Department of Industrial Engineering and Operations Research suggests that simplicity might be the key to navigating today’s complex markets.

In a recent study, Associate Professor Javad Lavaei, Professor Emeritus Max Shen, and PhD students Mengzi (Amy) Guo and Donghao Ying investigate how companies engaged in repeated price competition—such as in streaming, air travel, or e-commerce—can use simple, self-correcting algorithms to reach long-term pricing stability. At the heart of their model is a behavioral concept known as the reference effect, which captures how consumers’ willingness to pay is shaped not just by current prices, but by what they’ve seen or paid in the past.

Rather than rely on elaborate predictions or knowledge of their competitors’ strategies, firms in the study use a lightweight method called online projected gradient ascent (OPGA). With only their own sales feedback, they iteratively adjust prices over time. The result? Prices naturally converge toward a balanced state known as a stationary Nash equilibrium, where no company has a reason to change its strategy, achieving what researchers call no-regret learning.

The team also explored a more psychologically realistic scenario where consumers respond more strongly to price increases than to decreases, a behavior known as loss aversion. To handle this, they developed a more cautious version of the algorithm, dubbed conservative-OPGA. Even under these tougher conditions, companies were still able to adapt and stabilize their prices effectively.

Perhaps most striking is the real-world applicability of these methods. The algorithms don’t rely on full market visibility or perfect information—just the kind of limited, noisy feedback most businesses already have. As Professor Lavaei notes, “In an era of increasing uncertainty, it’s empowering to know that firms don’t need to outsmart the market. They just need to keep learning from their own experience.”

As industries search for pricing strategies that are adaptive, data-driven, and consumer-aware, this research offers a practical path forward, proving that stability doesn’t have to come at the cost of complexity.

Read the full research paper published in Management Science below.