EBay can’t claim to be the only one capable of bringing this vision to life. Along with others, Walmart is also making the move into digital retailing as fast as it can in an effort to compete with Amazon — and in a much more direct way. Walmart’s reputation in Silicon Valley is for a kind of old-school efficiency: getting pallets of goods (often from China) into a big-box store in America and then into the hands of its customers, all for very low prices. There are more than 200 million visits to its stores every week. But until fairly recently, Walmart’s online search engine was having trouble doing something as simple as identifying what visitors wanted when they searched for ‘‘denim.’’ And so two years ago the company opened @WalmartLabs, in Silicon Valley, where 1,500 people now work. There are an additional 1,000 people around the world dedicated solely to e-commerce. All of Walmart’s stores are now ‘‘geofenced’’ — that is, they know when individual customers are in the store, thanks to the Walmart app on their phones that can guide them to what they want. In roughly 220 of Walmart’s 4,000 locations, customers can make their purchases with their telephones, bypassing registers (and their lines) altogether. ‘‘People know Walmart as the world’s largest retailer, but they’re going to know us as one of the largest and fastest-growing e-commerce companies,’’ Neil Ashe, the head of global e-commerce at Walmart, said. This is corporate messaging, to be sure, but it also reflects a very real shift in strategy. Ashe has said elsewhere that turning Walmart into a digital retailer is not just a project but a permanent part of its future as a business.

“People expect Toys ‘R’ Us to act like Amazon,’’ said Christopher Saridakis, who heads eBay Enterprise, ‘‘but they don’t realize how hard it is.’’ He was preparing to show me around a 543,000-square-foot fulfillment center in a remote corporate complex in Walton, Ky. What he meant was that Amazon has conditioned consumers to expect an ease to online shopping — a few clicks, desired items always in stock, free two-day shipping and returns — that physical retailers have a hard time competing with. EBay Enterprise, which was known as GSI Commerce when eBay purchased it in 2011, now drives eBay’s effort to enable its larger retail partners to meet the same expectations.

Saridakis referred to the facility in Walton as ‘‘the other side of the computer’’: When we press ‘‘buy’’ on the websites of Levi’s or Aéropostale or Quicksilver or PBS or Major League Baseball, whose products are all warehoused in Walton, that purchase often becomes a package bound from Walton for your door. Five miles of conveyor belts feed into a double-tilt tray sorter that dumps individually wrapped goods into the appropriate chutes at one end of the facility and then packed-and-stamped boxes onto ramps that lead directly into UPS trucks at the other. Almost 200,000 products from nearly 600,000 unique locations within the facility make their way via human pickers and machine sorters into the proper packages and off to the people who want them.

EBay Enterprise also helps retailers rethink and reorganize how they use their physical stores. Increasingly, retailers are starting to regard their stores as small-scale distribution centers for their products, as nodes in the fulfillment process as well as showrooms. If you live in Manhattan and you order Beanie Babies online from Toys ‘‘R’’ Us, sometimes it makes more economic sense for an employee at a local Toys ‘‘R’’ Us to pack and ship that order than it does to have the fulfillment center in Kentucky do it. This takes an enormous amount of integrated technology to orchestrate, but it’s also the only way to compete with Amazon: using everything from physical stores to mobile applications to delivery services to make sure that customers can get what they want when they want it. Walmart is doing some of the same things: building million-square-foot online-only warehouses and experimenting with using stores as distribution centers. The company is now shipping goods directly from roughly 35 of its 4,000 stores.

While this process is about efficiently moving goods, the deeper purpose is to improve and manage the relationship with the customer. Healey Cypher, the head of retail innovation at eBay, tells a story about a bookseller who was convinced that online commerce would kill his business: ‘‘I said to him: ‘How do you know when someone’s in your store? You don’t, unless they bought something, and then only after the purchase. What if you had a platform for the first time ever that said, ‘‘This person is in your store, they like these things, they bought these things on your web store, and here’s an offer you should give them based on their purchases’’? You don’t have to take it, but you’ve never had that opportunity before.’ ’’

The best current example of the digital wallet’s promise, according to many in Silicon Valley, is Uber, a digital platform that connects riders and drivers. You enter your credit-card information into the Uber app once, and then every time you want to use it, the app knows where you are and shows you how many cars are nearby and how soon one can be available. You order with one touch on a mobile screen, and a text lets you know a driver is on the way and then another tells you when he’s near. He greets you by name, you tell him where you want to go and then, when you are dropped off, there is no further exchange — no tip, no receipt, no signing anything. The app takes care of all that for you. Uber didn’t change anything about the nature of cars or how they are driven. It just figured out how to use data and technology to make what was out there work much more efficiently. (EBay, through its acquisition of the company Shutl, has begun to exploit a similar inefficiency in the spare capacity of courier companies.)