We consider a cooperative Gaussian interference channel in which each receiver must decode its intended message locally, with the help of cooperation either at the receivers side or at the transmitter side. In the case of receiver cooperation, the receivers can process and share information through limited capacity backhaul links. In contrast to various previously considered distributed antenna architectures, where processing is utterly performed in a centralized fashion, the model considered in this paper aims to capture the essence of decentralized processing, allowing for a more general class of "interactive" interference management strategies. Focusing on the three-user case, we characterize the fundamental tradeoff between the achievable communication rates and the corresponding backhaul cooperation rate, in terms of degrees of freedom (DoF). Surprisingly, we show that the optimum communication-cooperation tradeoff per user remains the same when we move from two-user to three-user interference channels. In the absence of cooperation, this is due to interference alignment, which keeps the fraction of communication dimensions wasted for interference unchanged. When backhaul cooperation is available, we develop a new idea that we call cooperation alignment, which guarantees that the average (per user) backhaul load remains the same as we increase the number of users. In the case of transmitter cooperation, the transmitters can form their jointly precoded signals through an interactive protocol over the backhaul. In this case, we show that the optimal (per user) tradeoff between the achievable communication rates and the corresponding backhaul cooperation rate in the three-user case is the same as for receiver cooperation.