Businesses threatened by technology often respond by trying to get ahead of the new competition. Think of lucrative media companies that started giving away content online during the 1990s.

Many banks face similar dilemmas today, and one was cast in an unusually public light by a pair of recent announcements from Capital One Financial.

Capital One makes loans to the buyers of taxi medallions. For years, the price of medallions kept rising, peaking above $1 million in New York City, and Cap One's business looked strong.

But the market dynamics have shifted with the rising popularity of ride-sharing apps. Taxi medallion prices in New York have fallen by about 25% from their peak, according to a February research report from Sandler O'Neill.

On Thursday, Capital One Chief Executive Officer Richard Fairbank sounded a note of caution about the firm's medallion-lending portfolio, which holds less than $1 billion in loans.

"Medallion values have softened because of increased competition from new entrants like Uber. We continue to closely watch this sector," Fairbank said during an earnings call.

Just two days before, Capital One announced a credit card promotion that, ironically, puts additional pressure on its medallion-lending business.

Through April 2016, U.S. consumers will get a 20% discount on all Uber rides when they pay with a Capital One Quicksilver card, the McLean, Va., bank announced. In addition, certain Capital One customers who are new to Uber can get two free rides, worth up to a total of $60.

"You're actually partnering with someone who's cannibalizing some of your own business," said Sameer Gokhale, an analyst at Janney Montgomery Scott. "But if you don't do it, someone else might."

A Capital One spokeswoman did not respond to a question about which firm is bearing the cost of the credit card promotion. But Gokhale said that Uber is likely indifferent about which plastic card its riders use, and therefore has considerable leverage in negotiations with card issuers like Capital One.

"My view is that it's probably Capital One that's funding all or most of any discounts," he said.

The Uber promotion offers a new way for Capital One to market itself to tech-savvy millennials, said Christopher Donat, an analyst at Sandler O'Neill. "This might be an interesting way to acquire a younger demographic that has smartphones," he said.

Of course, the trade-off is that taxi companies, some of which rely on Capital One for financing, will get hurt by cheaper pricing for ride-sharing services.

Capital One got into the medallion-finance business in 2006 with its acquisition of North Fork Bank. As recently as November 2013, Capital One executives were touting the taxi market's resilience in the face of new competition.

But more recently, liquidity has dried up in the medallion-loan market. New York Community Bancorp has been trying to sell its portfolio of medallion loans, but the bank's executives said during their fourth-quarter earnings call that they have not yet been able to close a sale. (New York Community is scheduled to report first-quarter results on Wednesday.)

The liquidity crunch is the result of a gap between the taxi industry's loss of revenue, which so far has been relatively small, and perceptions about the industry's future, according to Andrew Murstein, president of Medallion Financial in New York. Shares in that company, which has been in the medallion business since the 1930s, have fallen by 19% in the last year.

"The earnings power of a cab has only dropped 4%, but the prices have come down 25%," Murstein said, referring to the cost of a taxi medallion.

Capital One did not respond to a question about whether it's interested in selling its medallion-finance business.