Foursquare is expanding its relationship with American Express to provide local deals to people who sync their cards to their Foursquare accounts. AmEx did a trial at SXSW , and that went well enough that it is rolling out the deals more broadly. The discounts, such as $20 off a $50 purchase at Sports Authority, are automatically applied to your AmEx account when you check in via Foursquare to a participating merchant before a purchase. Everyone in local commerce is trying to figure out how to close the loop between deals and payments. Once companies can tie mobile ads or deals to payments, they will be able to measure directly the sales generated by these mobile promotions. And one day that could potentially be a huge new business. But for now, it's making absolutely zilch for Foursquare, which remains a revenue-free zone.