TURN LEFT OFF the main reception to PayPal’s offices in San Jose, open a nondescript door and you step into a garish living room dominated by a flat-screen television. This is a laboratory for what PayPal calls “couch commerce”: people sit in front of the television buying things with their mobile phones or tablet computers. Next door is a make-believe shopping mall complete with a mock hardware store, grocery and coffee shop. In each, consumers can order, buy and pay for things using their phones, or even just their phone numbers.

The virtual mall and living room are exercise grounds for the next big battle in banking: over who will control the new digital wallets that will change the way in which people shop and spend—and, by implication, the way they save and borrow.