Postmates runs a network of couriers who, like Uber drivers, are dispatched by phones to deliver food, apparel, toothpaste and other goods from local stores in 18 American cities. The company recently announced a plan for retailers to build Postmates’ technology into their own technology systems, a way to give small stores the kind of logistical efficiencies that were previously available only to giants like Amazon.

As local retailers adopt such mobile innovations, customers will be able to search stores’ inventories, purchase goods for same-day delivery, and navigate and search for help and reviews inside a crowded store. None of these technologies pose an existential threat to Amazon, but by giving physical stores some of the conveniences that Amazon has long had, they may limit its potential reach.

“We want to use the city as our warehouse instead of building a warehouse outside the city,” Mr. Lehmann said. “We want to be part of a city versus saying, ‘Here’s a way that you can save $2 on an item, but nobody in your city earns a dime, but now you have a cheap DVD player — congratulations!’ ”

The Bay Area has become a hotbed for some of the most innovative retailing start-ups.

With Instacart, you can get groceries delivered instantly from big and small supermarkets. With Google’s Express delivery service, you can get household goods from big-box stores delivered on the same day you order. The app Curbside lets users order items from Target, and have them ready when they drive up to a store. And with Postmates, it is possible to order takeout, and pretty much anything else, and have it delivered directly very quickly.

These services all have in common speed and convenience: Because they route purchases from stores, they can often shuttle goods to buyers faster than they are available from Amazon. The prices are even competitive with Amazon, which delivers most of its products, even groceries, from warehouses that are a few hours away.

Image Amazon Fresh delivery trucks. The company has been investing vast sums in speeding up its delivery service, and it has been experimenting with ideas that mimic some of the start-ups, including using taxi-hailing apps to deliver goods. Credit... Kevork Djansezian/Getty Images

And speed changes everything.

I used to buy just about everything from Amazon; in 2012, my household recorded 141 purchases from the retailer, not including digital items like Kindle books. Many of these were for staples like paper towels and baby diapers. But when you run out of diapers, you can’t really wait a day or two to get them.