Might their solution be a merger? It may be nothing more than a rumor, but right now that's what people are talking about. The only evidence behind a supposed merger comes from a massive influx in Netflix stock value, along with some scattered information. Neither company has released an official statement - no surprise here, of course.
Smart move for Amazon? Netflix certainly is the leader in subscribed online video, to the point where numerous other services have been seeking to emulate them. They’ve also been willing to work with Amazon in the past, following the inclusion of Amazon Video on Demand through Roku. It may be that Netflix wants to grow faster than their capital can sustain, or it may be that Amazon wants to take the number one spot for online video. Their services don't currently conflict all that much, so it may be a smart move for both of them.