Zohar Gilad runs Fast Simon, a company that helps retailers optimize their websites. Instead of offering different prices, they might display higher-end items for customers with a free-spending buying history, and clearance items for bargain hunters. Targeted coupons for hesitant browsers also create a personalized price by another name, creating a sale that might not have happened.

“Say if you search for something and you didn’t buy it, you may get an email saying: ‘Hey, you have great taste. We saw you looking for black boots. Here’s a 20 percent coupon,’” Mr. Gilad said. “I think that personalization, done correctly, can be good and serve both shoppers and the merchants well.”

Nonetheless, some retailers prefer the loyalty that can stem from stable prices, even if it means forgoing short-term profits. Walmart, with its Every Day Low Prices approach, eschews coupons and rarely discounts anything. The practice “helps us earn trust with our customers, because they don’t have to chase sales and can count on us to consistently offer everyday low prices,” said Molly Blakeman, a Walmart spokeswoman.

Retailers also must take care to avoid the appearance of discrimination. The Princeton Review came under scrutiny when ProPublica revealed that because it charged higher rates for test preparation in certain ZIP codes, Asian American students tended to pay more than other groups. Researchers found that in Chicago, Uber’s and Lyft’s pricing algorithms resulted in higher fares in neighborhoods with more nonwhite residents. The companies said their pricing was based on demand patterns and not with any intent to discriminate.

The most important factor, said the Consumer Federation of America’s director of consumer protection, Erin Witte, is that shoppers understand the rules that merchants have created. Problems arise when there’s an “informational imbalance,” especially when it comes to something as existential as food, which may have fueled the Wendy’s backlash.

“When they feel like they can participate meaningfully in a negotiation about price, everyone understands on some level that a business is going to make money on a transaction,” Ms. Witte said. “But when you feel like you’re the subject of price manipulation that you as the consumer don’t have any access to, and certainly can’t predict with any measure of certainty, it just feels very unfair.”

Audio produced by Sarah Diamond.