Imagine working for an employer who, aware that you’re probably not sleeping enough at night, allows you to down tools and nap as part of your regular work duties – and not just forty winks at your desk, but a restorative snooze in a quiet room.

These are some of the measures being used by a growing number of companies in Japan to counter an epidemic of sleeplessness that costs its economy an estimated $138bn (£108bn) a year.

Tech startups have been quickest to address the “sleep debt” among irritable and unproductive employees.

Last year, Nextbeat, an IT service provider, went as far as setting up two “strategic sleeping rooms” – one for men, the other for women – at its headquarters in Tokyo. The aroma-infused rooms feature devices that block out background noise, allowing workers to stretch out on sofas for an undisturbed kip. Mobile phones, tablets and laptops are banned.

“Napping can do as much to improve someone’s efficiency as a balanced diet and exercise,” Emiko Sumikawa, a member of the Nextbeat board, told Kyodo news agency.

Nextbeat also asks employees leave work by 9pm and to refrain from doing excessive overtime, which has been blamed on a rising incidence of karoshi, or death from overwork.

One company even offers financial incentives to persuade its employees to shun overtime and get to bed at a reasonable hour. Crazy, a wedding planning company, awards employees who sleep at least six hours a night with points that can then be exchanged for food in the company cafeteria. Using an app to monitor their sleep, workers can accumulate points worth as much as 64,000 yen (£458) a year.

Japanese workers have more reason than most to submit to the urge for a daytime snooze, whether at work or during long commutes.

A survey conducted using fitness trackers in 28 countries found that Japanese men and women sleep, on average, just 6 hours and 35 minutes a night – 45 minutes less than the international average – making them the most sleep deprived of all.

Finnish women, by contrast, sleep almost an hour longer, with an average of 7.45 hours. Estonians, Canadians, Belgians, Austrians, as well as the Dutch and French, all get a comparatively decent night’s sleep, according to the survey.

A separate poll by the health products maker Fuji Ryoki found that 92.6% of Japanese over the age of 20 said they were not getting enough sleep.

Even weary workers whose employers have yet to officially sanction power naps at least know that resting their head on their desk for a few minutes probably won’t get them into trouble. Companies generally tolerate inemuri – or “sleeping while present” – as a demonstration of their employees’ commitment rather than as a sign of sloth, although nappers should generally remain seated and avoid appearing too comfortable.

The government has also come to appreciate the personal and professional benefits of a well-rested workforce, with the health ministry recommending that all working-age people take a nap of up to 30 minutes in the early afternoon – advice readily embraced by some of the country’s politicians.