If they achieve nothing else, though, such efforts could help remove barriers to price transparency, said Francois de Brantes, vice president at the Health Care Incentives Improvement Institute, a nonprofit that designs benefit programs.
"I think this could be quite the breakthrough," he said.
Yet de Brantes predicts only modest savings if shopping simply results in narrowing the price variation between high- and low-cost providers: "Ideally, transparency is about stopping folks from continuously charging more."
Among the programs in use, only a few show consumers the price differences among facilities. Many, like the one Cook used, merely display the financial incentives attached to each facility based on the underlying price.
Advocates say both approaches can work.
"When your plan members have 'skin in the game,' they have an incentive to consider the overall cost to the plan," said Catherine Keane, deputy commissioner of administrative services in New Hampshire. She credits the incentives with leading to millions of dollars in savings each year.
Several states require insurers or medical providers to provide cost estimates upon patients' requests, although studies have found that information can still be hard to access.
Now, private firms are marketing ways to make this information more available by incorporating it into incentive programs.
For example, Vitals, the New Hampshire-based company that runs the program Cook uses, and Healthcare Bluebook in Nashville offer employers -- for a fee -- comparative shopping gizmos that harness medical cost information from claims data. This information becomes the basis by which consumers shop around.
Maine's law, adopted last year, requires insurers that sell coverage to small businesses to offer financial incentives -- such as gift cards, discounts on deductibles or direct payments -- to encourage patients, starting in 2019, to shop around.