We now have research to show that companies need to embrace the core innovations of the collaborative economy if they want to thrive in the era of Kickstarter, Uber and Taskrabbit.

That’s the key insight of The New Rules of the Collaborative Economy, a report I co-authored with Jeremiah Owyang, which was released this week by Vision Critical and Crowd Companies.

When we authored the first large-scale study of collaborative economy customers eighteen months ago, we found lots of evidence that sharing was more than a hipster fad. It turned out that the customers of startups like Car2Go, Airbnb and Etsy look a lot like the population at large—and that their reasons for using on demand and peer-to-peer services predicted long-term growth.

Our latest report bears out that prediction. The total number of North Americans who have engaged in some form of sharing transaction has grown by 20% in that timeframe. Far more telling, almost every type of sharing has expanded: while buying and selling pre-owned goods was the only category of peer-to-peer transaction that attracted more than ten percent of the population in 2014, today there are many areas of the collaborative economy that engage that many people: custom products, personal and professional services, transportation, crowdfunding, learning and places to stay.

As peer-to-peer companies establish a firm place in many different parts of the economy, traditional businesses are recognizing that this new form of transaction represents a potential competitive threat. Will customers switch from sharing to buying? And just as crucial, is it possible to win them back if they do?

It turns out that most people are primed to make the shift to sharing if certain conditions are met. A majority of customers report that they would consider sharing instead of buying if it allows them to save 25% on their purchase—and among younger customers in particular, the vast majority are swayed by potential savings. About a third will switch from sharing to buying if it offers convenience—whether that’s in the form of delivery, ancillary services or customization. And just as many can be swayed if the sharing service offers them access to brand-name goods or services.

But the fact that so many customers can be wooed by sharing services shouldn’t make traditional companies give up hope. The factors that turn buyers into sharers can bring them back nearly (though not quite) as easily: a quarter of would-be sharers can be drawn back to conventional purchase transactions by the promise of convenience or a well-known brand. And even more people will switch from sharing to buying in pursuit of that 25% cost savings.

If established companies want to tap the power of price, convenience and brand as competitive advantages in the era of the collaborative economy, however, they will have to embrace the lessons of sharing startups’ success. Companies that want to compete on price need to launch their own peer-to-peer marketplaces—like Walmart’s aftermarket for used video games—in order to reduce their customers’ total cost of ownership. Companies that want to offer customers the benefit of convenience can provide the ancillary services and products they need—the way Home Depot now lets its customers rent tools and equipment. And companies that want to leverage the power of their existing brand to attract sharing customers need to find ways to offer their traditional products via ownership or access—just as BMW has done, by introducing the DriveNow service that lets people get BMW vehicles when and where they need them.

Nor do these competitive plays depend on starting your own sharing service. Partnering with collaborative economy startups can often be the fastest route to giving customers the savings, convenience or brand reliability they seek. Cosmo Hotel lets guests save on the cost of a big night out by making it easy for them to rent a dress from Rent the Runway, instead of buying their own. Whole Foods makes shopping more convenient for its customers by embracing Instacart as a way of giving its customers fast, easy deliveries. West Elm has lent Etsy customers the assurance of its well-known brand by selling Etsy products directly from its stores.

Of course, businesses don’t have to choose any of these paths. Hotels can stick with the rent-a-room model, retailers can continue to sell instead of rent, and manufacturers can produce take-it-or-leave-it products instead of custom goods. There’s still a core group of customers who want to get their products and services the way they always have, and who are still willing to pay a premium—or forego convenience—rather than rethink their patterns of consumption.

But those customers are dwindling. As our report shows, more and more people are embracing the new world of mobile enabled, peer-to-peer services that offer access instead of (or in addition to) ownership. The companies that thrive in this new world will be ones that not only recognize its risks, but embrace its opportunities.