“Amazon is showing it can fix the problem if it wants to,” Ms. Patten said.

The problem with list prices or, as they are sometimes called, manufacturers’ suggested retail prices, is that they are regularly more of a marketing concept than what anyone is actually charging. When Amazon was saying the list price of the Breville Infuser was $800, Breville itself was selling the machine for $500 — about the same as Amazon. Other retailers sell it for $500, too. Breville confirmed the price was $500.

Bargains online and offline that are not real bargains are breeding legal action, much of it using a tough California law against deceptive advertising. New cases have been filed in the last few months against Macy’s, J. Crew, Gymboree, Ann Taylor, Ralph Lauren and the website Wines ’Til Sold Out, according to TruthInAdvertising.org. Twenty-four cases were filed in the first six months of 2016, nearly as many as the 25 in all of 2015.

There have been at least 10 settlements. In April, a Los Angeles judge gave preliminary approval to a $6 million offer by Kohl’s Department Stores. That deal came on the heels of a $50 million preliminary settlement by J. C. Penney.

Amazon itself was the target of a fake-discounts suit — an unexpected development, because all Amazon customers agree to go to arbitration instead of court. A judge dismissed the complaint but the plaintiffs are now appealing, saying the arbitration clause is “unconscionable” and should be invalidated. Amazon declined to comment on the suit.

The shift away from list prices is taking some merchants on Amazon by surprise. A seller named Travis complained in an Amazon forum that the list price on his product — which he did not identify — had disappeared from the site. “I’m well aware that it is bogus but it is a common marketing tactic that works very well at boosting sales,” he wrote.

Amazon also appears to have stepped up its monitoring of a vendor system that allowed some sellers to insert data that listed their products as 99 percent or even 100 percent off. Another Amazon seller who complained that his list prices were not showing up said he was told by the retailer that it was routinely checking list prices on other sites.

Mr. Kovarik of Rout said his analysis indicated that Amazon was regularly eliminating more list prices. “In early May, about 29 percent of the products we saw were missing list prices, but now the number is up to about 70 percent,” he said.