Loyalty Goes Digital: A Look at Square Inc. Square, a mobile payment start-up, has been getting a lot of squawk lately. And for good reason. Square's latest innovation has to do with retail customer loyalty. How to attract it, how to enhance it, how to keep it. The company's apps now make it possible for shoppers to carry around digital loyalty cards, instead of the old style cards that got punched. You know, buy ten and get one free or at a steeply discounted price. The app that makes this happen is called Pay With Square, and is available for both iPhones and Android-based phones. The upgraded software lets merchants reward faithful customers by applying discounts automatically when they revisit the retail site or by granting points on a digital punch card each time they make a purchase. According to Square's COO, Keith Rabois, digital punch cards are more convenient than carrying around a wallet or purse full of paper cards, which, if you're like most people, you forget and leave at home. Then when you get to the store, you don't have it when you need it. With Pay With Square, your card is in your phone, one for each merchant. A number of companies are diving headfirst into the big pool of mobile payment processing. Surprisingly, the technology has been slower to catch on in the U.S. than in Europe and Asia. The problem is that U.S. consumers need to be convinced that mobile payments are as safe