It is widely expected that the core of next-generation cellular networks will be (i) based on software-defined networking (SDN) and network function virtualization (NFV), and (ii) shared between multiple parties, including traditional mobile operators and content providers. Such parties are normally competing with each other; however, they can obtain significant, mutual benefits even from limited and defined cooperation. We study how such a coopetition relationship influences the decisions of (i) how to place virtual network functions on physical hardware and (ii) how to steer traffic between them. We present an efficient, online algorithm to make such placement and steering decisions, and study its performance in a realistic scenario. We find that our algorithm would allow mobile operators and content providers to reduce their reliance on third-party vendors by 60%.