ONE of the big questions facing the business-travel industry is the extent to which it will embrace the sharing economy. Corporate-travel bookers, for example, are still deciding what they think about Airbnb. While road warriors seem to like staying in strangers' apartments, the suits back at HQ worry about booking their employees into places which have been subject to less stringent health-and-safety checks than the brand-name establishment next door. But companies do not appear to have the same qualms about ride-sharing. In the first quarter of 2016, services such as Uber and Lyft accounted for 46% of business “ground transportation” trips in America, according to Certify, an expense-management firm. That compares with 40% for car-hire and a piddling 14% for taxis. The share of business trips taken by taxi in America has dropped by 23 percentage points over the past two years.

Within the ride-sharing sector, Uber dominates. Stripping out those who hired a car, who are often travelling between cities, Uber has a 69% market share of business trips. Lyft has 4%. But Lyft’s share has been growing from that low base. Some think it is a company now on the up. It recently secured $1 billion in new investment, half of which came from General Motors. Apple announced in March that it had chosen the firm over Uber as its preferred way of ferrying staff around.

One of the things that appeals to business travellers about Lyft is the ability to book cars in advance, a service the firm unveiled earlier this year. With Uber, on the other hand, clients can only book a ride as and when they want it, and must hope that there is a driver nearby (although there nearly always is). That explains why Uber announced last week that it will follow Lyft's example and allow riders to book cars between 30 minutes and 30 days in advance.

All things being equal, that development will sound the death knell for taxis; expect cabs' share of the business market to diminish to almost nothing in the coming years. That will leave only one battle worth watching: that between Uber and Lyft. In all likelihood, only one will be left standing. As Om Malik, a startup-watcher, pointed out in the New Yorkerearlier this year, the importance of network effects means that most competition in Silicon Valley now leads towards one monopolistic winner. In the case of ride-sharing, helped by smartphones and algorithms, drivers will want to join the network with the most passengers, and passengers will want to use the network with the most drivers, creating a virtuous circle. If true, and despite Lyft's fightback, the odds must be on business travellers living in an Uber-only world a few years hence.