Mark Bertolini, chief executive officer of Aetna.

"If [our staff] can prove they get 20 nights of sleep for seven hours or more in a row, we will give them $US25 a night, up $US500 a year," said Mr Bertolini, who uses the wireless activity tracker Fitbit to monitor his employees' sleep levels.

"You can't be prepared if you're half-asleep," he said, citing research that better sleep can lead to bigger profits.

Working in collaboration with Duke University, Mr Bertolini said he had seen "69 minutes more a month of [worker] productivity on the part of us just investing in wellness and mindfulness".

World leaders have often prided themselves on their lack of sleep. Winston Churchill is said to have slept only five hours a night. Margaret Thatcher got four hours a night; former Italian prime minister Silvio Berlusconi said he needs only two hours.