On the Internet AS level topology, BGP policy routing is in charge of dictating the characteristics of routes which can be used for packet transmission. Furthermore the peculiarities of the BGP policies clearly affect the peering strategies of the ISP-s, hereby influencing the emerging topology. This paper takes a first step towards identifying the topological footprint issued by these policies. For this purpose we modify the framework of network formation games to support the most fundamental BGP policy called valley-free routing. We show the topological properties of the equilibrium topologies of this game in an analytical manner.